关于有限群的S-C置换嵌入子群的新探讨

A note on S-C-permutably embedded subgroups of finite groups

群G的子群H称为在G中S条件置换嵌入(简称S-C置换嵌入),如果对于任意的p∈π(H),H的每个Sy-lowp子群都是G的某个S条件置换子群的Sylowp子群.本文利用S-C置换嵌入子群,得到了有限群的一个新的特征性定理,并由此推广了一系列已知的结论.

A subgroup H of a group G is said to be S-conditionally permutably embedded（or in brevity, S-C-permutably embedded） in G, if for each p∈π（H） every Sylow p-subgroup of H is a Sylow p-subgroup of some S-conditionally permutable subgroup of G. By using the concept of S-C-permutably embedded subgroup, some new characterizations of finite groups are obtained, and several known results are generalized.