User:BudjarnLambeth/Basal subgroup - Revision history

BudjarnLambeth: BudjarnLambeth moved page Basal subgroup to User:BudjarnLambeth/Basal subgroup

2025-05-07T02:56:31Z

BudjarnLambeth moved page Basal subgroup to User:BudjarnLambeth/Basal subgroup

← Older revision	Revision as of 02:56, 7 May 2025
(No difference)

BudjarnLambeth at 14:06, 8 November 2024

2024-11-08T14:06:29Z

BudjarnLambeth: /* ed6/5, ed8/5, ed9/5, ed12/5... */

2024-11-06T09:15:46Z

ed6/5, ed8/5, ed9/5, ed12/5...

BudjarnLambeth: /* ed12/11, ed14/11, ed15/11, ed16/11... */ typo

2024-11-06T09:12:38Z

ed12/11, ed14/11, ed15/11, ed16/11...: typo

← Older revision		Revision as of 09:12, 6 November 2024
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	=== ed12/11, ed14/11, ed15/11, ed16/11... ===		=== ed12/11, ed14/11, ed15/11, ed16/11... ===
	A.k.a. "[[half-prime subgroup\|~~elevent~~-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|eleventh-prime subgroups]]".

	To find BSGn/11:		To find BSGn/11:

BudjarnLambeth: /* ed3/2, ed5/2, ed7/2, ed11/2... */

2024-11-05T13:11:14Z

ed3/2, ed5/2, ed7/2, ed11/2...

← Older revision		Revision as of 13:11, 5 November 2024
Line 31:		Line 31:
	=== ed3/2, ed5/2, ed7/2, ed11/2... ===		=== ed3/2, ed5/2, ed7/2, ed11/2... ===
	A.k.a. "[[half-prime subgroup]]s".		A.k.a. "[[half-prime subgroup]]s".


	To find BSGn/2:		To find BSGn/2:

BudjarnLambeth at 13:10, 5 November 2024

2024-11-05T13:10:58Z

← Older revision		Revision as of 13:10, 5 November 2024
Line 52:		Line 52:
	=== ed5/3, ed7/3, ed11/3, ed17/3... ===		=== ed5/3, ed7/3, ed11/3, ed17/3... ===
	A.k.a. "[[half-prime subgroup\|third-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|third-prime subgroups]]".


	To find BSGn/3:		To find BSGn/3:
Line 72:		Line 71:
	=== ed5/4, ed7/4, ed11/4, ed17/4... ===		=== ed5/4, ed7/4, ed11/4, ed17/4... ===
	A.k.a. "[[half-prime subgroup\|quarter-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|quarter-prime subgroups]]".


	To find BSGn/4:		To find BSGn/4:
Line 92:		Line 90:
	=== ed7/5, ed11/5, ed17/5, ed19/5... ===		=== ed7/5, ed11/5, ed17/5, ed19/5... ===
	A.k.a. "[[half-prime subgroup\|fifth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|fifth-prime subgroups]]".


	To find BSGn/5:		To find BSGn/5:
Line 111:		Line 108:
	=== ed7/6, ed11/6, ed17/6, ed19/6... ===		=== ed7/6, ed11/6, ed17/6, ed19/6... ===
	A.k.a. "[[half-prime subgroup\|sixth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|sixth-prime subgroups]]".


	To find BSGn/6:		To find BSGn/6:
Line 130:		Line 126:
	=== ed11/7, ed17/7, ed19/7, ed23/7... ===		=== ed11/7, ed17/7, ed19/7, ed23/7... ===
	A.k.a. "[[half-prime subgroup\|seventh-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|seventh-prime subgroups]]".


	To find BSGn/7:		To find BSGn/7:
Line 148:		Line 143:
	=== ed11/8, ed17/8, ed19/8, ed23/8... ===		=== ed11/8, ed17/8, ed19/8, ed23/8... ===
	A.k.a. "[[half-prime subgroup\|eighth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|eighth-prime subgroups]]".


	To find BSGn/8:		To find BSGn/8:
Line 166:		Line 160:
	=== ed11/9, ed17/9, ed19/9, ed23/9... ===		=== ed11/9, ed17/9, ed19/9, ed23/9... ===
	A.k.a. "[[half-prime subgroup\|ninth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|ninth-prime subgroups]]".


	To find BSGn/9:		To find BSGn/9:
Line 184:		Line 177:
	=== ed11/10, ed17/10, ed19/10, ed23/10... ===		=== ed11/10, ed17/10, ed19/10, ed23/10... ===
	A.k.a. "[[half-prime subgroup\|tenth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|tenth-prime subgroups]]".


	To find BSGn/10:		To find BSGn/10:
Line 202:		Line 194:
	=== ed13/11, ed17/11, ed19/11, ed23/11... ===		=== ed13/11, ed17/11, ed19/11, ed23/11... ===
	A.k.a. "[[half-prime subgroup\|eleventh-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|eleventh-prime subgroups]]".


	To find BSGn/11:		To find BSGn/11:
Line 219:		Line 210:
	=== ed13/12, ed17/12, ed29/12, ed23/12... ===		=== ed13/12, ed17/12, ed29/12, ed23/12... ===
	A.k.a. "[[half-prime subgroup\|twelfth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|twelfth-prime subgroups]]".


	To find BSGn/12:		To find BSGn/12:
Line 236:		Line 226:
	=== ed17/13, ed19/13, ed23/13, ed29/13... ===		=== ed17/13, ed19/13, ed23/13, ed29/13... ===
	A.k.a. "[[half-prime subgroup\|thirteenth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|thirteenth-prime subgroups]]".


	To find BSGn/13:		To find BSGn/13:
Line 252:		Line 241:
	=== ed17/14, ed19/14, ed23/14, ed29/14... ===		=== ed17/14, ed19/14, ed23/14, ed29/14... ===
	A.k.a. "[[half-prime subgroup\|fourteenth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|fourteenth-prime subgroups]]".


	To find BSGn/14:		To find BSGn/14:
Line 268:		Line 256:
	=== ed17/15, ed19/15, ed23/15, ed29/15... ===		=== ed17/15, ed19/15, ed23/15, ed29/15... ===
	A.k.a. "[[half-prime subgroup\|fifteenth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|fifteenth-prime subgroups]]".


	To find BSGn/15:		To find BSGn/15:
Line 336:		Line 323:
	=== ed4/3, ed8/3, ed10/3, ed14/3... ===		=== ed4/3, ed8/3, ed10/3, ed14/3... ===
	A.k.a. "[[half-prime subgroup\|third-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|third-prime subgroups]]".


	To find BSGn/3:		To find BSGn/3:
Line 363:		Line 349:
	=== ed9/4, ed15/4, ed21/4, ed25/4... ===		=== ed9/4, ed15/4, ed21/4, ed25/4... ===
	A.k.a. "[[half-prime subgroup\|quarter-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|quarter-prime subgroups]]".


	To find BSGn/4:		To find BSGn/4:
Line 384:		Line 369:
	=== ed6/5, ed8/5, ed9/5, ed12/5... ===		=== ed6/5, ed8/5, ed9/5, ed12/5... ===
	A.k.a. "[[half-prime subgroup\|fifth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|fifth-prime subgroups]]".


	To find BSGn/5:		To find BSGn/5:
Line 413:		Line 397:
	=== ed35/6, ed55/6, ed65/6, ed77/6... ===		=== ed35/6, ed55/6, ed65/6, ed77/6... ===
	A.k.a. "[[half-prime subgroup\|sixth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|sixth-prime subgroups]]".


	To find BSGn/6:		To find BSGn/6:
Line 433:		Line 416:
	=== ed8/7, ed9/7, ed10/7, ed12/7... ===		=== ed8/7, ed9/7, ed10/7, ed12/7... ===
	A.k.a. "[[half-prime subgroup\|seventh-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|seventh-prime subgroups]]".


	To find BSGn/7:		To find BSGn/7:
Line 463:		Line 445:
	=== ed9/8, ed15/8, ed21/8, ed25/8... ===		=== ed9/8, ed15/8, ed21/8, ed25/8... ===
	A.k.a. "[[half-prime subgroup\|eighth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|eighth-prime subgroups]]".


	To find BSGn/8:		To find BSGn/8:
Line 484:		Line 465:
	=== ed10/9, ed14/9, ed16/9, ed20/9... ===		=== ed10/9, ed14/9, ed16/9, ed20/9... ===
	A.k.a. "[[half-prime subgroup\|ninth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|ninth-prime subgroups]]".


	To find BSGn/9:		To find BSGn/9:
Line 508:		Line 488:
	=== ed21/10, ed27/10, ed33/10, ed39/10... ===		=== ed21/10, ed27/10, ed33/10, ed39/10... ===
	A.k.a. "[[half-prime subgroup\|tenth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|tenth-prime subgroups]]".


	To find BSGn/10:		To find BSGn/10:
Line 528:		Line 507:
	=== ed12/11, ed14/11, ed15/11, ed16/11... ===		=== ed12/11, ed14/11, ed15/11, ed16/11... ===
	A.k.a. "[[half-prime subgroup\|elevent-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|elevent-prime subgroups]]".


	To find BSGn/11:		To find BSGn/11:
Line 557:		Line 535:
	=== ed35/12, ed55/12, ed65/12, ed77/12... ===		=== ed35/12, ed55/12, ed65/12, ed77/12... ===
	A.k.a. "[[half-prime subgroup\|twelfth-prime subgroups]]".		A.k.a. "[[half-prime subgroup\|twelfth-prime subgroups]]".


	To find BSGn/12:		To find BSGn/12:

BudjarnLambeth at 13:09, 5 November 2024

2024-11-05T13:09:01Z

Show changes

BudjarnLambeth at 12:57, 5 November 2024

2024-11-05T12:57:54Z

← Older revision		Revision as of 12:57, 5 November 2024
Line 2:		Line 2:

	It is built on top of the concept of a [[half-prime subgroup]], so it is recommended to study half-prime subgroups first before exploring basal subgroups.		It is built on top of the concept of a [[half-prime subgroup]], so it is recommended to study half-prime subgroups first before exploring basal subgroups.

			The basal subgroup for equal divisions of n/m is named BSGn/m{{idiosyncratic}}. This makes it easy to refer to a specific BSG.

BudjarnLambeth: Document a concept that occured to me, based on CompactStar's half prime subgroups

2024-11-05T12:56:12Z

Document a concept that occured to me, based on CompactStar's half prime subgroups

Show changes

← Older revision		Revision as of 14:06, 8 November 2024
Line 308:		Line 308:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/2
	# Add n/2 to the start of the subgroup		# Add n/2 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 328:		Line 329:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/3
	# Add n/3 to the start of the subgroup		# Add n/3 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 354:		Line 356:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/4
	# Add n/4 to the start of the subgroup		# Add n/4 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 374:		Line 377:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/5
	# Add n/5 to the start of the subgroup		# Add n/5 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 402:		Line 406:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/6
	# Add n/6 to the start of the subgroup		# Add n/6 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 421:		Line 426:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/7
	# Add n/7 to the start of the subgroup		# Add n/7 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 450:		Line 456:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/8
	# Add n/8 to the start of the subgroup		# Add n/8 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 470:		Line 477:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/9
	# Add n/9 to the start of the subgroup		# Add n/9 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 493:		Line 501:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/10
	# Add n/10 to the start of the subgroup		# Add n/10 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 512:		Line 521:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/11
	# Add n/11 to the start of the subgroup		# Add n/11 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 540:		Line 550:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/12
	# Add n/12 to the start of the subgroup		# Add n/12 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 557:		Line 568:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/13
	# Add n/13 to the start of the subgroup		# Add n/13 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 582:		Line 594:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/14
	# Add n/14 to the start of the subgroup		# Add n/14 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a
Line 599:		Line 612:
	# Remove all instances of m/1 where m is a prime factor of n		# Remove all instances of m/1 where m is a prime factor of n
	# Remove all instances of m/1 where m is less than n's largest prime factor		# Remove all instances of m/1 where m is less than n's largest prime factor
			# Replace all instances of m/1 with m/15
	# Add n/15 to the start of the subgroup		# Add n/15 to the start of the subgroup
	# In all instances a/b where a<b, double a		# In all instances a/b where a<b, double a

← Older revision		Revision as of 09:15, 6 November 2024
Line 379:		Line 379:

	'''List:'''		'''List:'''
	* The basal subgroup of '''[[ed6/5]]''' - - - BSG6/5 - - - is 6~~/5 . 5~~/5 . 7/5 . 11/5 . 13/5 . 17/5...		* The basal subgroup of '''[[ed6/5]]''' - - - BSG6/5 - - - is 6/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5...
	* The basal subgroup of '''[[ed8/5]]''' - - - BSG8/5 - - - is 8~~/5 . 5~~/5 . 7/5 . 11/5 . 13/5 . 17/5...		* The basal subgroup of '''[[ed8/5]]''' - - - BSG8/5 - - - is 8/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5...
	* The basal subgroup of '''[[ed9/5]]''' - - - BSG9/5 - - - is 9~~/5 . 5~~/5 . 7/5 . 11/5 . 13/5 . 17/5...		* The basal subgroup of '''[[ed9/5]]''' - - - BSG9/5 - - - is 9/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5...
	* The basal subgroup of '''[[ed12/5]]''' - - - BSG12/5 - - - is 12~~/5 . 5~~/5 . 7/5 . 11/5 . 13/5 . 17/5...		* The basal subgroup of '''[[ed12/5]]''' - - - BSG12/5 - - - is 12/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5...
	* The basal subgroup of '''[[ed14/5]]''' - - - BSG14/5 - - - is 14/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5...		* The basal subgroup of '''[[ed14/5]]''' - - - BSG14/5 - - - is 14/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5...
	* The basal subgroup of '''[[ed16/5]]''' - - - BSG16/5 - - - is 16/5 . 3/5 . 5/5 . 7/5 . 11/5 . 13/5...		* The basal subgroup of '''[[ed16/5]]''' - - - BSG16/5 - - - is 16/5 . 3/5 . 7/5 . 11/5 . 13/5 . 17/5...
	* The basal subgroup of '''[[ed18/5]]''' - - - BSG18/5 - - - is 18~~/5 . 5~~/5 . 7/5 . 11/5 . 13/5 . 17/5...		* The basal subgroup of '''[[ed18/5]]''' - - - BSG18/5 - - - is 18/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5...
	* The basal subgroup of '''[[ed21/5]]''' - - - BSG21/5 - - - is 21/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5...		* The basal subgroup of '''[[ed21/5]]''' - - - BSG21/5 - - - is 21/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5...
	* The basal subgroup of '''[[ed22/5]]''' - - - BSG22/5 - - - is 22/5 . 13/5 . 17/5 . 19/5 . 23/5 . 29/5...		* The basal subgroup of '''[[ed22/5]]''' - - - BSG22/5 - - - is 22/5 . 13/5 . 17/5 . 19/5 . 23/5 . 29/5...
	* The basal subgroup of '''[[ed24/5]]''' - - - BSG24/5 - - - is 24~~/5 . 5~~/5 . 7/5 . 11/5 . 13/5 . 17/5...		* The basal subgroup of '''[[ed24/5]]''' - - - BSG24/5 - - - is 24/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5...
	* The basal subgroup of '''[[ed26/5]]''' - - - BSG26/5 - - - is 26/5 . 17/5 . 19/5 . 23/5 . 29/5 . 31/5...		* The basal subgroup of '''[[ed26/5]]''' - - - BSG26/5 - - - is 26/5 . 17/5 . 19/5 . 23/5 . 29/5 . 31/5...
	* The basal subgroup of '''[[ed27/5]]''' - - - BSG27/5 - - - is 27~~/5 . 5~~/5 . 7/5 . 11/5 . 13/5 . 17/5...		* The basal subgroup of '''[[ed27/5]]''' - - - BSG27/5 - - - is 27/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5...
	* The basal subgroup of '''[[ed28/5]]''' - - - BSG28/5 - - - is 28/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5...		* The basal subgroup of '''[[ed28/5]]''' - - - BSG28/5 - - - is 28/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5...
	''and so on...''		''and so on...''