Обобщенные модулярные подгруппы конечных групп и их применение

Abstract

A subgroup H of a group G is called modular in G if H is a modular element (in sense of Kurosh) of the lattice L(G) of all subgroups of G. The subgroup of H generated by all modular subgroups of G contained in H is called the modular core of H and denoted by HmG. In the paper, we introduce the following concept. A subgroup H of a group G is called m-supplemented in G if there exists a subgroup K of G such that G=HK and H ∩ K ≤ HmG. Based on this concept groups with m-supplemented maximal subgroups of Sylow subgroup were studied.