A Criterion for the σ-Subnormality of a Subgroup in a Finite 3'-Group

For any partition \(σ\) of the set \(P\) of all primes, it is proved that if a subgroup H of a finite \(3'\) -group G is \(σ\) -subnormal in \( \) for any \(x ∈ G\) , then H is \(σ\) -subnormal in G .