Bounding the maximal size of independent generating sets of finite groups
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 $G$.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2019
- DOI:
- 10.48550/arXiv.1908.01160
- arXiv:
- arXiv:1908.01160
- Bibcode:
- 2019arXiv190801160L
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Combinatorics
- E-Print:
- 11 pages