A NOTE ON WEAKLY -PERMUTABLY EMBEDDED AND WEAKLY -SUPPLEMENTED SUBGROUPS
CHANGWEN LI
Abstract
Suppose that is a finite group and is a subgroup of . is called weakly -permutably embedded in if there are a subnormal subgroup of and an -permutably embedded subgroup of contained in such that and ; is called weakly -supplemented in if there is a subgroup of such that and , where is the subgroup of generated by all those subgroups of which are -permutable in . We investigate the influence of weakly -permutably embedded and weakly -supplemented subgroups on the -nilpotency of finite groups. Some recent results are generalized.