Normal p-complement

In mathematical group theory, a normal p-complement of a finite group for a prime p is a normal subgroup of order coprime to p and index a power of p. In other words the group is a semidirect product of the normal p-complement and any Sylow p-subgroup.

Frobenius normal p-complement theorem

The Frobenius normal p-complement theorem states that if the normalizer of every non-trivial subgroup of a Sylow p-subgroup of G has a normal p-complement, then so does G.

References

• Gorenstein, D. (1980), Finite groups (2nd ed.), New York: Chelsea Publishing Co., ISBN 978-0-8284-0301-6, MR569209