## Finite 2-groups with odd number of conjugacy classes

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- by Andrei Jaikin-Zapirain and Joan Tent PDF
- Trans. Amer. Math. Soc.
**370**(2018), 3663-3688 Request permission

## Abstract:

In this paper we consider finite 2-groups with odd number of real conjugacy classes. On one hand we show that if $k$ is an odd natural number less than 24, then there are only finitely many finite $2$-groups with exactly $k$ 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-$p$ techniques, and, in particular, we use the Kneser classification of semi-simple $p$-adic algebraic groups.## References

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## Additional Information

**Andrei Jaikin-Zapirain**- Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, and Instituto de Ciencias Matemáticas - CSIC, UAM, UCM, UC3M, 28049 Madrid, Spain
- MR Author ID: 646902
- Email: andrei.jaikin@uam.es
**Joan Tent**- Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain
- MR Author ID: 911113
- Email: joan.tent@uv.es
- Received by editor(s): October 1, 2015
- Received by editor(s) in revised form: August 19, 2016
- Published electronically: December 27, 2017
- Additional Notes: This paper was partially supported by the grant MTM 2011-28229-C02-01 and MTM2014-53810-C2-01 of the Spanish MEyC and by the ICMAT Severo Ochoa project SEV-2011-0087

The second author was supported by PROMETEOII/2015/011 - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**370**(2018), 3663-3688 - MSC (2010): Primary 20D15; Secondary 20C15, 20E45, 20E18
- DOI: https://doi.org/10.1090/tran/7067
- MathSciNet review: 3766862