摘要
设F是一个群类．群G的子群H称为在G中F-S-可补的,如果存在G的一个子群K,使得G=HK且K/K∩HG∈F,其中HG=∩g∈GHg是包含在H中的G的最大正规子群．本文利用子群的F-S-可补性,给出了有限群的可解性,超可解性和幂零性的一些新的刻画．应用这些结果,我们可以得到一系列推论,其中包括有关已知的著名结果．
Let F be a class of groups. A subgroup H of a group G is called F-S-supplemented in G if there exists a subgroup K of G such that G=HK and K/K∩HG∈F, where HG=∩g∈GH^g is the maximal normal subgroup of G contained in H. In this paper, By using F-S-supplemented subgroups, we give some new criteria for the solvability, nilpotency and supersolvability of finite groups. By these results, we may get a series of corollaries, which contain some known results.
基金
国家自然科学基金(10471118#)
关键词
F-S-可补子群
可解群
幂零群
超可解群
F-S-supplemented subgroup
nilpotent group
supersolvable group
soluble group
