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math.GR2025
On finite groups with soluble centralisers
Valentina Grazian, Carmine Monetta, Gareth Tracey
We classify finite groups in which the centralisers of certain non-central elements are soluble. This includes a full structural description of groups whose non-central element cen…
math.GR2025
Groups with conjugacy classes of coprime sizes
Rachel D. Camina, Attila Maróti, Emanuele Pacifici +6
Suppose that , are elements of a finite group lying in conjugacy classes of coprime sizes. We prove that is an abelian nor…
math.GR2025
Subgroups of symmetric groups: enumeration and asymptotic properties
Colva M. Roney-Dougal, Gareth Tracey
In this paper, we prove that the symmetric group has subgroups, settling a conjecture of Pyber from 1993. We also derive asymptotically sharp upp…