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User:Lériendil/Third-superparticulars and semiparticulars by prime subgroup: Difference between revisions

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|-
|-
| G4 = R3
| G4 = R3
| '''2.5'''
| 2.5
| [[5/4]]
| [[5/4]]
| {{monzo| -2 1 }}
| {{monzo| -2 1 }}
|-
|-
| G5
| G5
| '''2.7'''
| 2.7
| [[8/7]]
| [[8/7]]
| {{monzo| 3 -1 }}
| {{monzo| 3 -1 }}
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|-
|-
| R6
| R6
| '''2.5.7'''
| 2.5.7
| [[50/49]]
| [[50/49]]
| {{monzo| 1 2 -2 }}
| {{monzo| 1 2 -2 }}
|-
|-
| G14
| G14
| '''2.5.13'''
| 2.5.13
| [[65/64]]
| [[65/64]]
| {{monzo| -6 1 1 }}
| {{monzo| -6 1 1 }}
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|}
|}


=== Higher primes ===
=== 2.3.13.p subgroups ===
{| class="wikitable center-1 center-2 center-5 center-6"
{| class="wikitable center-1 center-2 center-5 center-6"
|-
|-
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== 4-prime no-threes subgroups and 5-prime subgroups ==
== 4-prime no-threes subgroups and 5-prime subgroups ==
In the tables that follow, no-threes subgroups will be indicated in '''bold'''.


=== 7-add-one-limit (L7.p) ===
=== 5-add-two-limit (L5.p.q) ===
 
==== 7-add-one-limit (L7.p) ====
{| class="wikitable center-1 center-2 center-5 center-6"
|-
! rowspan="2" | Third-particular
! rowspan="2" | Subgroup
! colspan="2" | Comma
! rowspan="2" | Semiparticular
! rowspan="2" | Subgroup
! colspan="2" | Comma
|-
! Ratio
! Smonzo
! Ratio
! Smonzo
|-
|
|
|
|
| R9 = G23
| '''L11(-3)'''
| [[176/175]]
| {{monzo| 4 -2 -1 1 }}
|-
| G13
| '''L11(-3)'''
| [[56/55]]
| {{monzo| 3 -1 1 -1 }}
| R13
| [[11-limit|L11]]
| [[540/539]]
| {{monzo| 2 3 1 -2 -1 }}
|-
| G23 = R9
| '''L11(-3)'''
| [[176/175]]
| {{monzo| 4 -2 -1 1 }}
| R23 = S55
| [[11-limit|L11]]
| [[3025/3024]]
| {{monzo| -4 -3 2 -1 2 }}
|-
| G34
| [[11-limit|L11]]
| [[385/384]]
| {{monzo| -7 -1 1 1 1 }}
| R34 = S99
| [[11-limit|L11]]
| [[9801/9800]]
| {{monzo| -3 4 -2 -2 2 }}
|-
| G16
| L7.17
| [[85/84]]
| {{monzo| -2 -1 1 -1 1 }}
|
|
|
|
|-
| G19 = T15
| L7.17
| [[120/119]]
| {{monzo| 3 1 1 -1 -1 }}
| R19
| L7.17
| [[1701/1700]]
| {{monzo| -2 5 -2 1 -1 }}
|-
| G22
| '''2.5.7.23'''
| [[161/160]]
| {{monzo| -5 -1 1 1 }}
| R22
| L7.23
| [[2646/2645]]
| {{monzo| 1 3 -1 2 -2 }}
|-
| G47
| L7.23
| [[736/735]]
| {{monzo| 5 -1 -1 -2 1 }}
| R47 = S161
| L7.23
| [[25921/25920]]
| {{monzo| -6 -4 -1 2 2 }}
|-
| G29
| L7.31
| [[280/279]]
| {{monzo| 3 -2 1 1 -1 }}
| R29
| L7.31
| [[6076/6075]]
| {{monzo| 2 -2 -5 2 1 }}
|-
| G62
| L7.61
| [[1281/1280]]
| {{monzo| -8 1 -1 1 1 }}
| R62 = S244
| L7.61
| [[59536/59535]]
| {{monzo| 4 -5 -1 -2 2 }}
|-
| G82
| L7.83
| [[2241/2240]]
| {{monzo| -6 3 -1 -1 1 }}
| R82
| L7.83
| [[137781/137780]]
| {{monzo| -2 9 -1 1 -2 }}
|}
 
==== L5.11.p subgroups ====
{| class="wikitable center-1 center-2 center-5 center-6"
|-
! rowspan="2" | Third-particular
! rowspan="2" | Subgroup
! colspan="2" | Comma
! rowspan="2" | Semiparticular
! rowspan="2" | Subgroup
! colspan="2" | Comma
|-
! Ratio
! Smonzo
! Ratio
! Smonzo
|-
| G31
| '''2.5.11.29'''
| [[320/319]]
| {{monzo| 6 1 -1 -1 }}
| R31
| L5.11.29
| [[7425/7424]]
| {{monzo| -8 3 2 1 -1 }}
|-
| G46
| L5.11.47
| [[705/704]]
| {{monzo| -6 1 1 -1 1 }}
| R46
| L5.11.47
| [[24300/24299]]
| {{monzo| 2 5 2 -1 -2 }}
|-
| G98
| L5.11.97
| [[3201/3200]]
| {{monzo| -7 1 -2 1 1 }}
| R98 = S485
| L5.11.97
| [[235225/235224]]
| {{monzo| -3 -5 2 -2 2 }}
|-
| G241
| L5.11.239
| [[19360/19359]]
| {{monzo| 5 -4 1 2 -1 }}
| R241
| L5.11.239
| [[3499200/3499199]]
| {{monzo| 6 7 2 -4 -1 }}
|}
 
==== L5.13.p subgroups ====
{| class="wikitable center-1 center-2 center-5 center-6"
|-
! rowspan="2" | Third-particular
! rowspan="2" | Subgroup
! colspan="2" | Comma
! rowspan="2" | Semiparticular
! rowspan="2" | Subgroup
! colspan="2" | Comma
|-
! Ratio
! Smonzo
! Ratio
! Smonzo
|-
| G28
| L5.13.29
| [[261/260]]
| {{monzo| -2 2 -1 -1 1 }}
|
|
|
|
|-
| G38
| L5.13.37
| [[481/480]]
| {{monzo| -5 -1 -1 1 1 }}
| R38
| L5.13.37
| [[13690/13689]]
| {{monzo| 1 -4 1 -2 2 }}
|}
 
==== L5.17.p subgroups ====
{| class="wikitable center-1 center-2 center-5 center-6"
|-
! rowspan="2" | Third-particular
! rowspan="2" | Subgroup
! colspan="2" | Comma
! rowspan="2" | Semiparticular
! rowspan="2" | Subgroup
! colspan="2" | Comma
|-
! Ratio
! Smonzo
! Ratio
! Smonzo
|-
|
|
|
|
| R18
| '''2.5.17.19'''
| [[1445/1444]]
| {{monzo| -2 1 2 -2 }}
|-
| G49
| '''2.5.17.47'''
| [[800/799]]
| {{monzo| 5 2 -1 -1 }}
| R49
| L5.17.47
| [[29376/29375]]
| {{monzo| 6 3 -4 1 -1 }}
|-
| G52
| L5.17.53
| [[901/900]]
| {{monzo| -2 -2 -2 1 1 }}
|
|
|
|
|}
 
==== Higher-prime subgroups ====
{| class="wikitable center-1 center-2 center-5 center-6"
|-
! rowspan="2" | Third-particular
! rowspan="2" | Subgroup
! colspan="2" | Comma
! rowspan="2" | Semiparticular
! rowspan="2" | Subgroup
! colspan="2" | Comma
|-
! Ratio
! Smonzo
! Ratio
! Smonzo
|-
| G74
| L5.19.73
| [[1825/1824]]
| {{monzo| -3 -2 2 -1 1 }}
| R74
| L5.19.73
| [[101251/101250]]
| {{monzo| -1 -4 -4 1 2 }}
|-
| G73
| L5.37.71
| [[1776/1775]]
| {{monzo| 4 1 -2 1 -1 }}
| R73
| L5.37.71
| [[97200/97199]]
| {{monzo| 4 5 2 -2 -1 }}
|-
| G161
| L5.53.163
| [[8640/8639]]
| {{monzo| 6 3 1 -1 -1 }}
| R161
| L5.53.163
| [[1043200/1043199]]
| {{monzo| 8 -9 2 -1 1 }}
|-
| G242
| L5.61.241
| [[19521/19520]]
| {{monzo| -6 4 -1 -1 1 }}
| R242
| L5.61.241
| [[3542941/3542940]]
| {{monzo| -2 -11 -1 1 2 }}
|}
 
=== No-fives subgroups ===
 
==== 7-add-two-limit (2.3.7.p.q) ====
 
==== Higher primes ====


== See also ==
== See also ==
* [[User:Lériendil/Square_and_triangle_superparticulars_by_prime_subgroup|Square and triangle superparticulars by prime subgroup]]
* [[User:Lériendil/Square_and_triangle_superparticulars_by_prime_subgroup|Square and triangle superparticulars by prime subgroup]]
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