On \(\pi\)-quasinormal subgroups in finite groups
This is basically a continuation of earlier work by the author, K. Corradi and L. Hethelyi; two theorems are proved. Theorem 1. If A and B are \(\pi\)-quasinormal subgroups of finite group G (for some set \(\pi\) of primes), if \(G=AB\), and if A and B are \(\pi\)-separable, then G is also \(\pi\)-separable. Theorem 2. If A and B are q-quasinormal subgroups of finite group G, if \(G=AB\), and if A and B are in N(p,q) then G is also in N(p,q). Here N(p,q), for distinct primes p and q, denotes the class of finite groups in which a p-subgroup is normalized by a q-subgroup exactly when it is centralized by it. There are additional results, such as Lemma 5. If A and B are \(\pi\)-quasinormal subgroups of finite group G with \(AB=BA\) then \(A\cap B\) is also \(\pi\)-quasinormal in G.
scientific article; zbMATH DE number 4114869
scientific article