20 research outputs found
On groups with a class-preserving outer automorphism
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