Lemma on containment in p'-core for Thompson transitivity theorem
From Groupprops
Statement
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 .
Related facts
Applications
Facts used
References
- Finite Groups by Daniel Gorenstein, ISBN 0821843427, Page 289, Theorem 5.1, ^{More info}