From Surf Wiki (app.surf) — the open knowledge base
P-constrained group
Type of finite group
Type of finite group
In mathematics, a p-constrained group is a finite group resembling the centralizer of an element of prime order p in a group of Lie type over a finite field of characteristic p. They were introduced by in order to extend some of Thompson's results about odd groups to groups with dihedral Sylow 2-subgroups.
Definition
If a group has trivial p core Op(G), then it is defined to be p-constrained if the p-core Op(G) contains its centralizer, or in other words if its generalized Fitting subgroup is a p-group. More generally, if Op(G) is non-trivial, then G is called p-constrained if G/Op(G) is p-constrained.
All p-solvable groups are p-constrained.
References
This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.
Ask Mako anything about P-constrained group — get instant answers, deeper analysis, and related topics.
Research with MakoFree with your Surf account
Create a free account to save articles, ask Mako questions, and organize your research.
Sign up freeThis content may have been generated or modified by AI. CloudSurf Software LLC is not responsible for the accuracy, completeness, or reliability of AI-generated content. Always verify important information from primary sources.
Report