G. Glauberman

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20182026

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math.GR2026

Splitting the center of a Sylow subgroup

George Glauberman, Justin Lynd

Suppose $p$ is a prime and $S$ is a Sylow $p$ -subgroup of a finite group $G$ . If $S$ is normal in $G$ , then $Z (S)$ is the direct product of $S \cap Z (G)$ with $[Z (S), G]$ . We prove…

math.GR2019

Centers of Sylow Subgroups and Automorphisms

George Glauberman, Robert Guralnick, Justin Lynd +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-g…

math.GR2018

Splitting the center of a Sylow subgroup

Centers of Sylow Subgroups and Automorphisms

More on a question of M. Newman on isomorphic subgroups of solvable groups