A probabilistic version of a theorem of lászló kovács and hyo-seob sim
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 $1/e.$ Let $G$ be a finite soluble group. {Assume} that for every $p\in \pi(G)$ there exists $G_p\leq G$ such...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2020-03-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | https://ijgt.ui.ac.ir/article_23073_26232b99d2d66bbcad0f18ccab2e0578.pdf |
| Summary: | 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 $1/e.$ 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 ${\mathcal V}(G)\leq d+7.$ |
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| ISSN: | 2251-7650 2251-7669 |