Subgroup rank of a group

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This article defines an arithmetic function on groups
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Definition

Suppose G is a group. Then, the subgroup rank of G is defined as the supremum, over all subgroups H of G, of the minimum size of generating set of H.

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.

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