Конечные группы с заданными системами квазиперестановочных подгрупп

Abstract

Let A be a subgroup of a group G, K ≤ H ≤ G. Then we say that A covers or avoids the pair (K, H) if either AH = AK or A ∩ H = A ∩ K. The pair (K, H) is called a maximal pair of G if K is a maximal subgroup of H. We say that: (1) A is quasipermutable in G if A either covers or avoids every maximal pair (K, H) of G; (2) A is weakly quasipermutable in G if G has a subgroup T and a quasipermutable subgroup C such that G = AT and T ∩ A ≤ C ≤ A. Based on these concepts new characterizations of finite groups are obtained.