What the study found
The study 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, where a Sylow torus is a maximal torus tied to a prime divisor condition in groups of Lie type.
Why the authors say this matters
The authors say the work is motivated by the recent character correspondence conjecture of Moretó and Rizo. They also state that it is motivated by the question of whether quasi-semiregular elements exist in finite permutation groups.
What the researchers tested
The paper studies finite quasi-simple groups of Lie type and examines semisimple elements of prime power order. The authors determine subnormalisers and investigate maximal overgroups of normalisers of Sylow tori.
What worked and what didn't
The abstract states that the subnormalisers are determined for the elements under study. It also states that the maximal overgroups of normalisers of Sylow tori are determined; it does not describe any unsuccessful cases or exceptions.
What to keep in mind
The available summary is limited to the abstract, so no detailed methods, examples, or exceptions are provided. The abstract does not state broader consequences beyond the motivating questions.
Key points
- Subnormalisers of semisimple elements of prime power order are determined.
- The setting is finite quasi-simple groups of Lie type.
- Maximal overgroups of normalisers of Sylow tori are also determined.
- The work is motivated by a character correspondence conjecture of Moretó and Rizo.
- The abstract also mentions quasi-semiregular elements in finite permutation groups as motivation.
Disclosure
- Research title:
- Subnormalisers of semisimple elements in finite groups are determined
- Authors:
- Gunter Malle
- Institutions:
- University of Kaiserslautern
- Publication date:
- 2026-04-22
- OpenAlex record:
- View
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