What the study found
The paper determines the subnormalisers of semisimple elements of prime power order in finite quasi-simple groups of Lie type. It also determines the maximal overgroups of normalisers of Sylow tori.
Why the authors say this matters
The authors say the work is motivated by the recent character correspondence conjecture by Moretó and Rizo and by the question of whether quasi-semiregular elements exist in finite permutation groups.
What the researchers tested
The study focuses on finite quasi-simple groups of Lie type and on semisimple elements of prime power order. The authors examine subnormalisers and maximal overgroups of normalisers of Sylow tori.
What worked and what didn't
The abstract states that the subnormalisers were determined. It also states that the maximal overgroups of normalisers of Sylow tori were determined. No negative result or failed case is described in the available abstract.
What to keep in mind
The abstract does not give the detailed proofs, case distinctions, or exact classifications. It also does not state limitations beyond the scope to finite quasi-simple groups of Lie type and semisimple elements of prime power order.
Key points
- The paper determines subnormalisers of semisimple elements of prime power order.
- The groups considered are finite quasi-simple groups of Lie type.
- The paper also determines maximal overgroups of normalisers of Sylow tori.
- The authors link the work to a character correspondence conjecture by Moretó and Rizo.
- The abstract does not describe any failed cases or explicit limitations beyond its stated scope.
Disclosure
- Research title:
- Subnormalisers of semisimple elements are determined
- Authors:
- Gunter Malle
- Institutions:
- University of Kaiserslautern
- Publication date:
- 2026-04-22
- OpenAlex record:
- View
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