Comptes Rendus
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/

[1] William Burnside Theory of Groups of Finite Order, Dover Publications, 1955 | MR

[2] Lynne M. Butler A unimodality result in the enumeration of subgroups of a finite abelian group, Proc. Am. Math. Soc., Volume 101 (1987) no. 4, pp. 771-775 | DOI | MR | Zbl

[3] Jean Delsarte Fonctions de Möbius sur les groupes abeliens finis, Ann. Math., Volume 49 (1948), pp. 600-609 | DOI | Zbl

[4] Walter Feit; John G. Thompson Solvability of groups of odd order, Order, Volume 13 (1963), pp. 775-1029 | MR | Zbl

[5] Philip Hall A note on soluble groups, J. Lond. Math. Soc., Volume 3 (1928), pp. 98-105 | DOI | MR | Zbl

[6] Philip Hall The eulerian functions of a group, Q. J. Math., Oxf. Ser., Volume 7 (1936), pp. 134-151 | DOI

[7] Kurt A. Hirsch On a theorem of Burnside, Q. J. Math., Volume 1 (1950), pp. 97-99 | DOI | MR | Zbl

[8] John Poland Two problems of finite groups with k conjugate classes, J. Aust. Math. Soc., Volume 8 (1968), pp. 49-55 | DOI | MR | Zbl

[9] Helmut Wielandt Zum Satz von Sylow, Math. Z., Volume 60 (1954), pp. 407-408 | DOI | MR | Zbl

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