Abelian supplements in almost simple groups
Let G be an almost simple group with socle $G_0$ . In this paper we prove that whenever $G/G_0$ is abelian, then there exists an abelian subgroup A of G such that $G=AG_0$ . We propose a few applications of this structural property of almost simple groups.
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001609/type/journal_article |
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| author | Mauro Costantini Andrea Lucchini Daniele Nemmi |
| author_facet | Mauro Costantini Andrea Lucchini Daniele Nemmi |
| author_sort | Mauro Costantini |
| collection | DOAJ |
| description | Let G be an almost simple group with socle
$G_0$
. In this paper we prove that whenever
$G/G_0$
is abelian, then there exists an abelian subgroup A of G such that
$G=AG_0$
. We propose a few applications of this structural property of almost simple groups. |
| format | Article |
| id | doaj-art-ae52089fed3c4d0cba726a216f14c0f3 |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-ae52089fed3c4d0cba726a216f14c0f32025-01-24T05:20:19ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2024.160Abelian supplements in almost simple groupsMauro Costantini0Andrea Lucchini1https://orcid.org/0000-0002-2134-4991Daniele Nemmi2Università di Padova, Dipartimento di Matematica “Tullio Levi-Civita”, Via Trieste 63, 35121 Padova, Italy; E-mail:Università di Padova, Dipartimento di Matematica “Tullio Levi-Civita”, Via Trieste 63, 35121 Padova, ItalyUniversità di Padova, Dipartimento di Matematica “Tullio Levi-Civita”, Via Trieste 63, 35121 Padova, Italy; E-mail:Let G be an almost simple group with socle $G_0$ . In this paper we prove that whenever $G/G_0$ is abelian, then there exists an abelian subgroup A of G such that $G=AG_0$ . We propose a few applications of this structural property of almost simple groups.https://www.cambridge.org/core/product/identifier/S2050509424001609/type/journal_article20D0620D45 |
| spellingShingle | Mauro Costantini Andrea Lucchini Daniele Nemmi Abelian supplements in almost simple groups Forum of Mathematics, Sigma 20D06 20D45 |
| title | Abelian supplements in almost simple groups |
| title_full | Abelian supplements in almost simple groups |
| title_fullStr | Abelian supplements in almost simple groups |
| title_full_unstemmed | Abelian supplements in almost simple groups |
| title_short | Abelian supplements in almost simple groups |
| title_sort | abelian supplements in almost simple groups |
| topic | 20D06 20D45 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001609/type/journal_article |
| work_keys_str_mv | AT maurocostantini abeliansupplementsinalmostsimplegroups AT andrealucchini abeliansupplementsinalmostsimplegroups AT danielenemmi abeliansupplementsinalmostsimplegroups |