Counting maximal abelian subgroups of p-groups

I. M. Isaacs; Lior Yanovski

doi:10.1007/s00013-022-01739-9

Counting maximal abelian subgroups of p-groups

I. M. Isaacs^*, Lior Yanovski

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We show that the number of maximal abelian subgroups of a finite p-group is congruent to 1 modulo p. Furthermore, if p> 2 , the same can be said for the maximal elementary abelian subgroups, and more generally, for the maximal abelian subgroups of any given p-power exponent.

Original language	English
Pages (from-to)	1-9
Number of pages	9
Journal	Archiv der Mathematik
Volume	119
Issue number	1
DOIs	https://doi.org/10.1007/s00013-022-01739-9
State	Published - Jul 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022, Springer Nature Switzerland AG.

Keywords

Exponent of group
Maximal abelian subgroup
p-group

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10.1007/s00013-022-01739-9

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KW - Exponent of group

KW - Maximal abelian subgroup

KW - p-group

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Counting maximal abelian subgroups of p-groups

Abstract

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Keywords

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