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2-groups with few conjugacy classes

Published online by Cambridge University Press:  20 January 2009

Nigel Boston  and
Judy L. Walker
Nigel Boston
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA (boston@math.uiuc.edu)
Judy L. Walker
Affiliation:
Department of Mathematics and Statistics, University of Nebraska, Lincoln, NB 68588, USA (jwalker@math.unl.edu)
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Abstract

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An old question of Brauer that asks how fast numbers of conjugacy classes grow is investigated by considering the least number cn of conjugacy classes in a group of order 2n. The numbers cn are computed for n ≤ 14 and a lower bound is given for c15. It is observed that cn grows very slowly except for occasional large jumps corresponding to an increase in coclass of the minimal groups Gn. Restricting to groups that are 2-generated or have coclass at most 3 allows us to extend these computations.

Keywords

p-groupsconjugacy classescoclass
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 1 , February 2000 , pp. 211 - 217
Copyright
Copyright © Edinburgh Mathematical Society 2000

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