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math.GR2025
On the number and sizes of double cosets of Sylow subgroups of the symmetric group
Persi Diaconis, Eugenio Giannelli, Robert M. Guralnick +4
Let be a Sylow -subgroup of the symmetric group . We investigate the number and sizes of the double cosets, showing that most double cosets…
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
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…