Frontiers of Mathematics in China >
On subgroups of finite groups
Received date: 23 Oct 2009
Accepted date: 08 Mar 2010
Published date: 05 Dec 2010
Copyright
Let G be a finite group, and let be a formation of finite groups. We say that a subgroup H of G is 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 -hypercenter of G/HG. In this paper, we obtain some results about the subgroups and then use them to study the structure of finite groups.
Key words:
Finite group;
Xiuxian FENG , Wenbin GUO . On subgroups of finite groups[J]. Frontiers of Mathematics in China, 2010 , 5(4) : 653 -664 . DOI: 10.1007/s11464-010-0062-0
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