Title of article :
New Characterizations of Some Classes of Finite Groups
Author/Authors :
Guo, Wenbin University of Science and Technology of China - Department of Mathematics, China , Guo, Wenbin Xuzhou Normal University - Department of Mathematics, China , Feng, Xiuxian Xuzhou Normal University - Department of Mathematics, China , Huang, Jianhong University of Science and Technology of China - Department of Mathematics, China , Huang, Jianhong Xuzhou Normal University - Department of Mathematics, China
Abstract :
Let G be a finite group and F a formation of finite groups. We say that a subgroup H of G is Fh-normal in G if there exists a normal subgroup T of G such that HT is a normal Hall subgroup of G and (H∩T)HG/HG is contained in the F-hypercenter ZF∞(G/HG) of G/HG. In this paper, we obtain some results about the Fh-normal subgroups and use them to study the structure of finite groups. Some new characterizations of supersoluble groups, soluble groups and p-nilpotent groups are obtained and some known results are generalized.
Keywords :
Finite groups , Fh , normal subgroups , Sylow subgroups , maximal subgroups , minimal subgroups
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
