no. G9
Théorie des groupes
Congruences associated with families of nilpotent subgroups and a theorem of Hirsch
Aivazidis, Stefanos1  ; Müller, Thomas2
1Department of Mathematics & Applied Mathematics, University of Crete, Greece
2Department of Mathematics, University of Vienna, Austria
Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, 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.

Reçu le :
Révisé le :
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DOI : 10.5802/crmath.514
Classification : 20D20, 20D60
Keywords: Nilpotent systems of subgroups, congruences

Aivazidis, Stefanos  1   ; Müller, Thomas  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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Aivazidis, Stefanos; Müller, Thomas. Congruences associated with families of nilpotent subgroups and a theorem of Hirsch. Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, pp. 1585-1592. doi: 10.5802/crmath.514

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