Minimum size of generating set
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Definition
Let G be a group. The minimum size of generating set for G, often called the rank or generating set-rank of G, and sometimes denoted d(G) or r(G), is defined as the minimum possible size of a generating set for G.
This number is finite if and only if the group is a finitely generated group.
Related notions
- Subgroup rank of a group: This is the maximum of the generating set-ranks over all subgroups of the group.
- Rank of a p-group: For a group of prime power order, this is the maximum of the ranks of all the abelian subgroups of the group.
