A probabilistic version of a theorem of lászló kovács and hyo-seob sim
Publish place: International Journal of Group Theory، Vol: 9، Issue: 1
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_THEGR-9-1_002
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
For a finite group group, denote by $\mathcal V(G)$ the smallest positive integer $k$ with the property that the probability of generating $G$ by $k$ randomly chosen elements is at least $۱/e.$ Let $G$ be a finite soluble group. {Assume} that for every $p\in \pi(G)$ there exists $G_p\leq G$ such that $p$ does not divide $|G:G_p|$ and ${\mathcal V}(G_p)\leq d.$ Then ${\mathcal V}(G)\leq d+۷.$
Keywords:
Finite soluble groups , generation of finite groups
Authors
Andrea Lucchini
Dipartimento di Matematica Università di Padova
Mariapia Moscatiello
Dipartimento di Matematica Università di Padova