Two-groups with few conjugacy classes

Authors

Nigel Boston, University of Illinois at Urbana-ChampaignFollow
Judy L. Walker, University of Nebraska - LincolnFollow

Document Type

Article

Date of this Version

2000

Citation

Published in Proceedings of the Edinburgh Mathematical Society 43 (2000), pp 211-217.

doi 10.1017/S0013091500020824

Comments

Copyright 2000 Edinburgh Mathematical Society; published by Cambridge University Press. Used by permission.

Abstract

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