Bounding the maximal size of independent generating sets of finite groups
arXiv:1908.01160
summary
The authors bound the maximal size of a minimal generating set of a finite group using the sum of the minimal numbers of generators of its Sylow subgroups.
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 $\sum_{p\in Ï(G)}d_p(G),$ where we are denoting by $d_p(G)$ the minimal number of generators of a Sylow $p$-subgroup of $G$ and by $Ï(G)$ the set of prime numbers dividing the order of $G$.
11 pages
Topics & keywords
#finite groups#generating sets#Sylow subgroups#minimal generators#group invariantsm(G)d_p(G)Sylow p-subgroupindependent generating setmaximal size bound