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math.GR2024
Characterizing inner automorphisms and realizing outer automorphisms
Benjamin Sambale
We give elementary proofs of the following two theorems on automorphisms of a finite group G: (1) An automorphism of G is inner if and only if it extends to an automorphism of ever…
math.GR2024
Groups with supersolvable automorphism group
Benjamin Sambale
We call a finite group G ultrasolvable if it has a characteristic subgroup series whose factors are cyclic. It was shown by Durbin--McDonald that the automorphism group of an ultra…
math.GR2024
On a fixed point formula of Navarro-Rizo
Benjamin Sambale
Let G be a pi-separable group with a Hall pi-subgroup H or order n. For x in H let lambda(x) be the number of Hall pi-subgroups of G containing x. We show that $\prod_{d\mid n}\pro…