Characterizing finite solvable groups through the nilpotency probability
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914448392847360 |
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| author | Lucchini, Andrea |
| author_facet | Lucchini, Andrea |
| contents | Given a finite group $G$, we denote by $ν(G)$ the probability that two randomly chosen elements of $G$ generate a nilpotent subgroup. We prove that if $ν(G)>1/12,$ then $G$ is solvable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04534 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterizing finite solvable groups through the nilpotency probability Lucchini, Andrea Group Theory Given a finite group $G$, we denote by $ν(G)$ the probability that two randomly chosen elements of $G$ generate a nilpotent subgroup. We prove that if $ν(G)>1/12,$ then $G$ is solvable. |
| title | Characterizing finite solvable groups through the nilpotency probability |
| topic | Group Theory |
| url | https://arxiv.org/abs/2604.04534 |