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关于F-S-可补子群
  • 期刊名称：数学研究与评论，2007， 27（1）， 207－211.
  • 时间：0
  • 分类：O152.1[理学—数学;理学—基础数学]
  • 作者机构：[1]徐州师范大学数学系,江苏徐州221116, [2]中国科学技术大学数学系,安徽合肥230026
  • 相关基金：国家自然科学基金（10471118#）
  • 相关项目：群的Sylow对象及相关公开问题研究
作者： 李长稳，郭文彬，
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
中文摘要：

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∈GH^g是包含在打中的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．

英文摘要：

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.

同期刊论文项目
群的Sylow对象及相关公开问题研究
期刊论文 62 会议论文 26 著作 1
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