Groups with a solvable subgroup of prime-power index
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866915717105844224 |
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| author | Bastos, Raimundo Schneider, Csaba |
| author_facet | Bastos, Raimundo Schneider, Csaba |
| contents | In this paper we describe some properties of groups $G$ that contain a solvable subgroup of finite prime-power index (Theorem 1 and Corollaries 2--3). We prove that if $G$ is a non-solvable group that contains a solvable subgroup of index $p^α$ (for some prime $p$), then the quotient $G/\mbox{rad}(G)$ of $G$ over the solvable radical is asymptotically small in comparison to $p^α!$ (Theorem 4). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_16414 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Groups with a solvable subgroup of prime-power index Bastos, Raimundo Schneider, Csaba Group Theory 20D05, 20D10, 20D20 In this paper we describe some properties of groups $G$ that contain a solvable subgroup of finite prime-power index (Theorem 1 and Corollaries 2--3). We prove that if $G$ is a non-solvable group that contains a solvable subgroup of index $p^α$ (for some prime $p$), then the quotient $G/\mbox{rad}(G)$ of $G$ over the solvable radical is asymptotically small in comparison to $p^α!$ (Theorem 4). |
| title | Groups with a solvable subgroup of prime-power index |
| topic | Group Theory 20D05, 20D10, 20D20 |
| url | https://arxiv.org/abs/2006.16414 |