Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Finite 2-groups with odd number of conjugacy classes
HTML articles powered by AMS MathViewer

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


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.
Similar Articles
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:
  • Joan Tent
  • Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain
  • MR Author ID: 911113
  • Email:
  • 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:
  • MathSciNet review: 3766862