Denote by m(G) the largest size of a minimal generating set of a finite group G. We estimate m(G) in terms of Σpϵπ(G) dp(G), where we are denoting by dp(G) the minimal number of generators of a Sylow p-subgroup of G and by π(G) the set of prime numbers dividing the order of G.
Bounding the maximal size of independent generating sets of finite groups
Lucchini A.;Moscatiello M.;Spiga P.
2021
Abstract
Denote by m(G) the largest size of a minimal generating set of a finite group G. We estimate m(G) in terms of Σpϵπ(G) dp(G), where we are denoting by dp(G) the minimal number of generators of a Sylow p-subgroup of G and by π(G) the set of prime numbers dividing the order of G.
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