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2009-07-31T20:26:57Z

Created page with '{{arithmetic function on groups}} ==Definition== Suppose <math>G</math> is a group. Then, the '''subgroup rank''' of <math>G</math> is defined as the supremum, over all sub…'

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{{arithmetic function on groups}}

==Definition==

Suppose <math>G</math> is a [[group]]. Then, the '''subgroup rank''' of <math>G</math> is defined as the supremum, over all subgroups <math>H</math> of <math>G</math>, of the [[minimum size of generating set]] of <math>H</math>.

If the subgroup rank of a group is finite, then the group is a [[slender group]], i.e., every subgroup of it is a [[finitely generated group]].

==Related notions==

* [[Minimum size of generating set]]

Subgroup rank of a group - Revision history

Vipul: Created page with '{{arithmetic function on groups}} ==Definition== Suppose G is a group. Then, the '''subgroup rank''' of G is defined as the supremum, over all sub…'

Vipul: Created page with '{{arithmetic function on groups}} ==Definition== Suppose $G$ is a group. Then, the '''subgroup rank''' of $G$ is defined as the supremum, over all sub…'