Analogue of Thompson transitivity theorem fails for abelian subgroups of rank two
It is possible to choose a finite group and a prime number such that is a group in which every p-local subgroup is p-constrained, such that:
There exists a subgroup of that is maximal among abelian normal subgroups in some -Sylow subgroup of , such that has rank two, and there is a prime such that is not transitive on the collection of maximal -invariant -subgroups of .
In other words, the analogue of the Thompson transitivity theorem fails if we drop the assumption of rank at least three.
- Thompson transitivity theorem
- Analogue of Thompson transitivity theorem fails for groups in which not every p-local subgroup is p-constrained