Groupprops, The Group Properties Wiki (pre-alpha)
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Subgroup rank of a group
From Groupprops
This article defines an arithmetic function on groups
View other such arithmetic functions
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.
Related notions
