English

Finite 2-groups with odd number of conjugacy classes

Group Theory 2016-11-29 v1

Abstract

In this paper we consider finite 2-groups with odd number of real conjugacy classes. On one hand we show that if kk is an odd natural number less than 24, then there are only finitely many finite 2-groups with exactly kk real conjugacy classes. On the other hand we construct infinitely many finite 2-groups with exactly 25 real conjugacy classes. Both resuls are proven using pro-pp techniques and, in particular, we use the Kneser classification of semi-simple pp-adic algebraic groups.

Keywords

Cite

@article{arxiv.1611.09077,
  title  = {Finite 2-groups with odd number of conjugacy classes},
  author = {Andrei Jaikin-Zapirain and Joan Tent},
  journal= {arXiv preprint arXiv:1611.09077},
  year   = {2016}
}

Comments

26 pages; to be published on Trans. Amer. Math. Soc

R2 v1 2026-06-22T17:06:11.509Z