The maximal size of a minimal generating set

نویسندگان

چکیده

Abstract A generating set for a finite group G is minimal if no proper subset generates , and $m(G)$ denotes the maximal size of . We prove conjecture Lucchini, Moscatiello Spiga by showing that there exist $a,b> 0$ such any satisfies $m(G) \leqslant \cdot \delta (G)^b$ $\delta (G) = \sum _{p \text { prime}} m(G_p)$ where $G_p$ Sylow p -subgroup To do this, we first bound all almost simple groups Lie type (until now, nontrivial bounds were known except rank $1$ or $2$ ). In particular, r over field $\mathbb {F}_{p^f}$ $r + \omega (f) m(G) a(r (f))^b$ $\omega (f)$ number distinct prime divisors f process, confirm Gill Liebeck base faithful primitive action an has at most $ar^b

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ژورنال

عنوان ژورنال: Forum of Mathematics, Sigma

سال: 2023

ISSN: ['2050-5094']

DOI: https://doi.org/10.1017/fms.2023.71