Lemma on containment in p'-core for Thompson transitivity theorem
Suppose is a finite group that is a group in which every p-local subgroup is p-constrained. Suppose is maximal among abelian normal subgroups in a -Sylow subgroup of , and is not cyclic, i.e., .
Suppose is a prime number distinct from , and is an -invariant -subgroup of . Suppose is a subgroup of for which the p-core is nontrivial, and , then .
- Maximal among abelian normal subgroups in p-Sylow subgroup that is not cyclic implies every invariant p'-subgroup is in the p'-core in p-constrained group