Comptes Rendus
Group theory
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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.514
Classification: 20D20, 20D60
Keywords: 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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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

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