English

On groups with a class-preserving outer automorphism

Group Theory 2016-11-25 v1

Abstract

In 1911, Burnside asked whether or not there exist groups that have an outer automorphism which preserves conjugacy classes. Two years later he answered his own question by constructing a family of such groups. Using the small group library in MAGMA we determine all of the groups of order n < 512 that possess such an automorphism. Our investigations led to the discovery of four new infinite families of such groups, all of which are 2-groups of coclass 4.

Keywords

Cite

@article{arxiv.1310.7663,
  title  = {On groups with a class-preserving outer automorphism},
  author = {Peter A. Brooksbank and Matthew S. Mizuhara},
  journal= {arXiv preprint arXiv:1310.7663},
  year   = {2016}
}
R2 v1 2026-06-22T01:56:08.412Z