Comptes Rendus
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Théorie des groupes
Congruences associated with families of nilpotent subgroups and a theorem of Hirsch
Stefanos Aivazidis1  ; Thomas Müller2
1 Department of Mathematics & Applied Mathematics, University of Crete, Greece
2 Department of Mathematics, University of Vienna, Austria
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1585-1592.

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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DOI : 10.5802/crmath.514
Classification : 20D20, 20D60
Mots clés : Nilpotent systems of subgroups, congruences

Stefanos Aivazidis 1 ; Thomas Müller 2

1 Department of Mathematics & Applied Mathematics, University of Crete, Greece
2 Department of Mathematics, University of Vienna, Austria
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Stefanos Aivazidis; Thomas Müller. Congruences associated with families of nilpotent subgroups and a theorem of Hirsch. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1585-1592. doi : 10.5802/crmath.514. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.514/

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