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 is an odd natural number less than 24, then there are only finitely many finite 2-groups with exactly 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- techniques and, in particular, we use the Kneser classification of semi-simple -adic algebraic groups.
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