Weakly C~#-Normality Of Subgroups And The Structure Of Finite Groups

The thesis introduces the weakly c~#-normality of subgroups by weakeningthe conditions of the c~#-normality. Besides, we studied the influence of theirsubgroups on the solvability, p-solvability, p-supersolvability and p-nilpotency offinite groups.In chapter one, we studied the influence of the weakly c~#-normality of sub-groups on the solvability of finite groups. We introduce the weakly c~#-normalityof subgroups. By using the weakly c~#-normality of some maximal,2-maximaland Hall subgroups, we obtain several criteria on the solvability of finite groups.The obtained results improve, unify and generalize some recent related results ofsome authors.Chapter two deals with the influence of the new characteristic of the maximalsubgroups of Sylow subgroups of groups on the p-supersolvability of finite group.Chapter three obtained two sufcient or necessary conditions on the p-nilpotencyof finite groups by studying the weakly c~#-normality of maximal and minimalsubgroups of finite groups.