The Fω-normalizers of finite groups

Аннотация

Given a nonempty set ω of primes and a nonempty formation F of finite groups, we define the F^ω-normalizer in a finite group and study their properties (existence, invariance under certain homomorphisms, conjugacy, embedding, and so on) in the case that F is an ω-local formation. We so develop the results of Carter, Hawkes, and Shemetkov on the F-normalizers in groups.