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Bounding the maximal size of independent generating sets of finite groups

Part of: Representation theory of groups Permutation groups

Published online by Cambridge University Press:  24 January 2020

Andrea Lucchini ,
Mariapia Moscatiello  and
Pablo Spiga
Andrea Lucchini
Affiliation:
Dipartimento di Matematica ‘Tullio Levi-Civita’, University of Padova, Via Trieste 53, 35121Padova, Italy (lucchini@math.unipd.it; mariapia.moscatiello@math.unipd.it)
Mariapia Moscatiello
Affiliation:
Dipartimento di Matematica ‘Tullio Levi-Civita’, University of Padova, Via Trieste 53, 35121Padova, Italy (lucchini@math.unipd.it; mariapia.moscatiello@math.unipd.it)
Pablo Spiga
Affiliation:
Dipartimento di Matematica Pura e Applicata, University of Milano-Bicocca, Via Cozzi 55, 20126Milano, Italy (pablo.spiga@unimib.it)
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Abstract

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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.

Keywords

Generating setsNumber of generators

MSC classification

Primary: 20D99: None of the above, but in this section
Secondary: 20B05: General theory for finite groups 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 1 , February 2021 , pp. 133 - 150
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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