In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for...In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for non-chief factor,there is no study up to now.The purpose of this paper is to build the theory.Let A be a subgroup of a finite group G and Σ:G0≤G1≤…≤Gn some subgroup series of G.Suppose that for each pair(K,H) such that K is a maximal subgroup of H and G i 1 K < H G i for some i,either A ∩ H = A ∩ K or AH = AK.Then we say that A is Σ-embedded in G.In this paper,we study the finite groups with given systems of Σ-embedded subgroups.The basic properties of Σ-embedded subgroups are established and some new characterizations of some classes of finite groups are given and some known results are generalized.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11071229)Chinese Academy of Sciences Visiting Professorship for Senior International Scientists (Grant No.2010T2J12)
文摘In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for non-chief factor,there is no study up to now.The purpose of this paper is to build the theory.Let A be a subgroup of a finite group G and Σ:G0≤G1≤…≤Gn some subgroup series of G.Suppose that for each pair(K,H) such that K is a maximal subgroup of H and G i 1 K < H G i for some i,either A ∩ H = A ∩ K or AH = AK.Then we say that A is Σ-embedded in G.In this paper,we study the finite groups with given systems of Σ-embedded subgroups.The basic properties of Σ-embedded subgroups are established and some new characterizations of some classes of finite groups are given and some known results are generalized.