Institution: | Department of Mathematics, Zhongshan University, Guangzhou 510275, China and Department of Mathematics, Guangxi Teacher's College, Nanning, 530001, China ; Lingnan College and Department of Mathematics, Zhongshan University, Guangzhou, 510275, China ; Department of Mathematics, Guangdong College of Education, Guangzhou, 510310, China |
Abstract: | This paper proves: Let be a saturated formation containing . Suppose that is a group with a normal subgroup such that . (1) If all maximal subgroups of any Sylow subgroup of are -supple- mented in , then ; (2) If all minimal subgroups and all cyclic subgroups with order 4 of are -supplemented in , then . |