Let A be a subgroup of a group G and X a nonempty subset of G. A is called an X-semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T 1 of T there exists an element x ∈ X such that ...Let A be a subgroup of a group G and X a nonempty subset of G. A is called an X-semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T 1 of T there exists an element x ∈ X such that AT 1 x = T 1 x A. On the basis of this concept we obtain some new characterizations of finite supersoluble groups.展开更多
In this paper, we give some new conditions of the existence of Hall subgroups in non-soluble finite groups, and so the famous Hall theorem and Schur-Zassenhaus theorem are generalized.
基金the National Natural Science Foundation of China (Grant No.10771180) a postgraduate innovation grant of University of Science and Technology of China
文摘Let A be a subgroup of a group G and X a nonempty subset of G. A is called an X-semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T 1 of T there exists an element x ∈ X such that AT 1 x = T 1 x A. On the basis of this concept we obtain some new characterizations of finite supersoluble groups.
基金The research is supported by the NNSF of China （Grant 11371335） and the Natural Science Foundation of Shandong Province （Grant ZR2014AL001）, China.
文摘In this paper, we give some new conditions of the existence of Hall subgroups in non-soluble finite groups, and so the famous Hall theorem and Schur-Zassenhaus theorem are generalized.
