Analogue of Thompson transitivity theorem fails for groups in which not every p-local subgroup is p-constrained
From Groupprops
Statement
It is possible to choose a finite group and a prime number such that is not a group in which every p-local subgroup is p-constrained, and such that:
There is a subgroup that is maximal among abelian normal subgroups in some -Sylow subgroup of such that the rank of is at least three, and there is a prime such that is not transitive on the set of maximal -invariant -subgroups.
In other words, the analogue of the Thompson transitivity theorem fails if we drop the assumption that the group is a group in which every p-local subgroup is p-constrained.
Related facts
- Thompson transitivity theorem
- Analogue of Thompson transitivity theorem fails for abelian subgroups of rank two
References
Textbook references
- Finite Groups by Daniel Gorenstein, ISBN 0821843427, Page 299, Exercise 7, Chapter 8, ^{More info}