Robert Guralnick, Gabriel Navarro
Published 2019-01-21Version 1
Suppose that p is an odd prime and G is a finite group having no normal non-trivial p'-subgroup. We show that if a is an automorphism of G of p-power order centralizing a Sylow p-group of G, then a is inner. This answers a conjecture of Gross.
Orbits in Extra-special $p$-Groups for $p$ an Odd Prime
On a Question of Glasby, Praeger, and Xia
Conjugacy for certain automorphisms of the one-sided shift via transducers
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