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arXiv · 1310.7663

On groups with a class-preserving outer automorphism

Peter A. Brooksbank·Matthew S. Mizuhara
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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.

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Peter A. Brooksbank, Matthew S. Mizuhara. 2013-10-29. On groups with a class-preserving outer automorphism. https://arxiv.org/abs/1310.7663

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