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Bounding the maximal size of independent generating sets of finite groups
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 1 / February 2021
- Published online by Cambridge University Press:
- 24 January 2020, pp. 133-150
- Print publication:
- February 2021
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- Article
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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 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.
