Counting maximal abelian subgroups of p-groups

I. M. Isaacs*, Lior Yanovski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)1-9
Number of pages9
JournalArchiv der Mathematik
Volume119
Issue number1
DOIs
StatePublished - Jul 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, Springer Nature Switzerland AG.

Keywords

  • Exponent of group
  • Maximal abelian subgroup
  • p-group

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