Groups with conjugacy classes of coprime sizes
Abstract Suppose that , are elements of a finite group lying in conjugacy classes of coprime sizes. We prove that is an abelian normal subgroup of and, as a consequence, that if and are ‐regular elements for some set of primes , then is a ‐regular conjugacy class in . The latter statement was previously known for ‐separable groups and this generalisation permits us to extend several results concerning the common divisor graph on ‐regular conjugacy classes, for some prime .
Authors
- Gareth Tracey (ORCID: https://orcid.org/0000-0001-7588-702X)
- Emanuele Pacifici (ORCID: https://orcid.org/0000-0001-8159-5584)
- Christopher Parker (ORCID: https://orcid.org/0000-0003-3437-2876)
- Martin van Beek (ORCID: https://orcid.org/0000-0003-1465-0242)
- V. Sotomayor
- K. Rekvényi
- J. Saunders
- R. D. Camina
- A. Maróti
Institutions
- HUN-REN Alfréd Rényi Institute of Mathematics (HU)
- Universidad de Granada (ES)
- University of Cambridge (GB)
- University of Manchester (GB)
- University of Bristol (GB)
- University of Warwick (GB)
- Heilbronn Institute for Mathematical Research (GB)
- University of Florence (IT)
- University of Birmingham (GB)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2026-02-25
- DOI
- https://doi.org/10.1112/blms.70320
- Citations
- 1
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 122.31
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni
- Division of Mathematical Sciences