the NSF of China(Nos.11201082,11471054,11671063),the NSF of Jiangsu Province(No.BK20161265);Cultivation Program for Outstanding Young College Teachersof Guangdong Province(Yq2013061).
Let G be a finite group.Let D={(g,g)|g∈C},the main diagonalsubgroup of G x G.In this paper,we consider the suitable generalized normalities orindex of D in G x G,some interesting results are obtained.
supported by National Natural Science Foundation of China (Grant Nos. 11201082 and 11171353);China Postdoctoral Science Foundation (Grant Nos. 2012M521724 and 2013T60866);Natural Science Foundation of Guangdong Province (Grant No. S201204007267)
Let G be a finite group,and H a subgroup of G.H is called s-permutably embedded in G if each Sylow subgroup of H is a Sylow subgroup of some s-permutable subgroup of G.In this paper,we use s-permutably embedding prope...