A generating set S for a group G is independent if the subgroup generated by is properly contained in G for all We describe the structure of finite groups G such that there are precisely two numbers appearing as the cardinalities of independent generating sets for G.
Lucchini, A., Spiga, P. (2023). FINITE GROUPS WITH INDEPENDENT GENERATING SETS OF ONLY TWO SIZES. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 108(3), 449-458 [10.1017/S0004972723000126].
FINITE GROUPS WITH INDEPENDENT GENERATING SETS OF ONLY TWO SIZES
Spiga P.
2023
Abstract
A generating set S for a group G is independent if the subgroup generated by is properly contained in G for all We describe the structure of finite groups G such that there are precisely two numbers appearing as the cardinalities of independent generating sets for G.
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