Counting maximal abelian subgroups of p-groups

Isaacs, I. M.; Yanovski, Lior

doi:10.1007/s00013-022-01739-9

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Counting maximal abelian subgroups of p-groups

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Yanovski, Lior
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00013-022-01739-9
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Citation

Isaacs, I. M., & Yanovski, L. (2022). Counting maximal abelian subgroups of p-groups. Archiv der Mathematik, 119(1), 1-9. doi:10.1007/s00013-022-01739-9.

Cite as: https://hdl.handle.net/21.11116/0000-000A-A936-B

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.