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.
Lucchini, A., Moscatiello, M., Spiga, P. (2021). Bounding the maximal size of independent generating sets of finite groups. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 151(1), 133-150 [10.1017/prm.2020.6].
Bounding the maximal size of independent generating sets of finite groups
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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