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== Generators in math and JI subgroups ==

A [[Wikipedia: Generating set of a group|set of '''generators''']], or '''generating set''', for a [[Wikipedia: Group ~~%28mathematics%29~~|group]] (such as a [[JI subgroup]] or a temperament thereof) is a subset of the elements of the group which is not contained in any [[Wikipedia: Subgroup|proper subgroup]], which is to say, any subgroup which is not the whole group. If the set is a finite set, the group is called finitely generated. If it is also an [[Wikipedia: Abelian group|abelian group]], it is called a [[Wikipedia: Finitely generated abelian group|finitely generated abelian group]].

A [[Wikipedia: Generating set of a group|set of '''generators''']], or '''generating set''', for a [[Wikipedia: Group (mathematics)|group]] (such as a [[JI subgroup]] or a temperament thereof) is a subset of the elements of the group which is not contained in any [[Wikipedia: Subgroup|proper subgroup]], which is to say, any subgroup which is not the whole group. If the set is a finite set, the group is called finitely generated. If it is also an [[Wikipedia: Abelian group|abelian group]], it is called a [[Wikipedia: Finitely generated abelian group|finitely generated abelian group]].

A '''basis''' (plural ''bases'') is a minimal generating set, i.e. a generating set which has no "redundant" or "unnecessary" generators. For example, {2, 3, 5} and {2, 3, 5/3} are bases for the JI subgroup 2.3.5. However, {2, 3, 5, 15} is not a basis: 15 = 3*5 so we can take out 15 from this generating set.

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 == Generators in math and JI subgroups ==
-A [[Wikipedia: Generating set of a group|set of '''generators''']], or '''generating set''', for a [[Wikipedia: Group %28mathematics%29|group]] (such as a [[JI subgroup]] or a temperament thereof) is a subset of the elements of the group which is not contained in any [[Wikipedia: Subgroup|proper subgroup]], which is to say, any subgroup which is not the whole group. If the set is a finite set, the group is called finitely generated. If it is also an [[Wikipedia: Abelian group|abelian group]], it is called a [[Wikipedia: Finitely generated abelian group|finitely generated abelian group]].
+A [[Wikipedia: Generating set of a group|set of '''generators''']], or '''generating set''', for a [[Wikipedia: Group (mathematics)|group]] (such as a [[JI subgroup]] or a temperament thereof) is a subset of the elements of the group which is not contained in any [[Wikipedia: Subgroup|proper subgroup]], which is to say, any subgroup which is not the whole group. If the set is a finite set, the group is called finitely generated. If it is also an [[Wikipedia: Abelian group|abelian group]], it is called a [[Wikipedia: Finitely generated abelian group|finitely generated abelian group]].
 A '''basis''' (plural ''bases'') is a minimal generating set, i.e. a generating set which has no "redundant" or "unnecessary" generators. For example, {2, 3, 5} and {2, 3, 5/3} are bases for the JI subgroup 2.3.5. However, {2, 3, 5, 15} is not a basis: 15 = 3*5 so we can take out 15 from this generating set.