Congruences associated with families of nilpotent subgroups and a theorem of Hirsch
Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number of a finite group of odd order.
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.514/ |
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| author | Aivazidis, Stefanos Müller, Thomas |
| author_facet | Aivazidis, Stefanos Müller, Thomas |
| author_sort | Aivazidis, Stefanos |
| collection | DOAJ |
| description | Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number of a finite group of odd order. |
| format | Article |
| id | doaj-art-2415963baf8340abb5c6286aad877f34 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-2415963baf8340abb5c6286aad877f342025-02-07T11:10:51ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G91585159210.5802/crmath.51410.5802/crmath.514Congruences associated with families of nilpotent subgroups and a theorem of HirschAivazidis, Stefanos0Müller, Thomas1Department of Mathematics & Applied Mathematics, University of Crete, GreeceDepartment of Mathematics, University of Vienna, AustriaOur main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number of a finite group of odd order.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.514/Nilpotent systems of subgroupscongruences |
| spellingShingle | Aivazidis, Stefanos Müller, Thomas Congruences associated with families of nilpotent subgroups and a theorem of Hirsch Comptes Rendus. Mathématique Nilpotent systems of subgroups congruences |
| title | Congruences associated with families of nilpotent subgroups and a theorem of Hirsch |
| title_full | Congruences associated with families of nilpotent subgroups and a theorem of Hirsch |
| title_fullStr | Congruences associated with families of nilpotent subgroups and a theorem of Hirsch |
| title_full_unstemmed | Congruences associated with families of nilpotent subgroups and a theorem of Hirsch |
| title_short | Congruences associated with families of nilpotent subgroups and a theorem of Hirsch |
| title_sort | congruences associated with families of nilpotent subgroups and a theorem of hirsch |
| topic | Nilpotent systems of subgroups congruences |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.514/ |
| work_keys_str_mv | AT aivazidisstefanos congruencesassociatedwithfamiliesofnilpotentsubgroupsandatheoremofhirsch AT mullerthomas congruencesassociatedwithfamiliesofnilpotentsubgroupsandatheoremofhirsch |