# Analogue of Thompson transitivity theorem fails for groups in which not every p-local subgroup is p-constrained

## Statement

It is possible to choose a finite group $G$ and a prime number $p$ such that $G$ is not a group in which every p-local subgroup is p-constrained, and such that:

There is a subgroup $A$ that is maximal among abelian normal subgroups in some $p$-Sylow subgroup of $G$ such that the rank of $A$ is at least three, and there is a prime $q \ne p$ such that $C_G(A)$ is not transitive on the set of maximal $A$-invariant $q$-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.