Counting maximal abelian subgroups of p-groups

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.

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Bibliographic Details
Published in:Archiv der Mathematik 2022-07, Vol.119 (1), p.1-9
Main Authors: Isaacs, I. M., Yanovski, Lior
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Subgroups
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Description
Summary: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.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-022-01739-9