Bounding the maximal size of independent generating sets of finite groups

Andrea Lucchini; Mariapia Moscatiello; Pablo Spiga

Bounding the maximal size of independent generating sets of finite groups

Group Theory 2019-08-06 v1 Combinatorics

Authors: Andrea Lucchini , Mariapia Moscatiello , Pablo Spiga

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 $\sum_{p\in \pi(G)}d_p(G),$ where we are denoting by $d_p(G)$ the minimal number of generators of a Sylow $p$ -subgroup of $G$ and by $\pi(G)$ the set of prime numbers dividing the order of $G$ .

Keywords

finite groups minimal generating set Sylow p-subgroup maximal size prime divisors group order

Cite

@article{arxiv.1908.01160,
  title  = {Bounding the maximal size of independent generating sets of finite groups},
  author = {Andrea Lucchini and Mariapia Moscatiello and Pablo Spiga},
  journal= {arXiv preprint arXiv:1908.01160},
  year   = {2019}
}

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11 pages

Bounding the maximal size of independent generating sets of finite groups

Abstract

Keywords

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