Let G be a group and G=G_(1)G_(2) where G_(i) are subgroups of G.In this paper,we investigate the structure of G under the conditions that some subgroups of G_(i) are subnormal in G.
In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
Denote the class of finite groups that are the product of two normal supersoluble subgroups and the class of groups that are the product of two subnormal supersoluble subgroups by B_(1)and B_(2),respectively.In this p...Denote the class of finite groups that are the product of two normal supersoluble subgroups and the class of groups that are the product of two subnormal supersoluble subgroups by B_(1)and B_(2),respectively.In this paper,a characterisation of groups in B_(1)or in B_(2)is given.By applying this new characterisation,some new properties of B_(1)(B_(2))and new proofs of many known results about B_(1)or B_(2)are obtained.Further,closure properties of B_(1)and B_(2)are discussed.展开更多
Based on Wielandt＇s criterion for subnormality of subgroups in finite groups, we study 2-maximal subgroups of finite groups and present another subnormality criterion in finite solvable groups.
For a finite group G, let S（G） be the set of minimal subgroups of odd order,which are complemented in G. It is proved that if every minimal subgroup X of odd orderof G which does not belong to S（G）, CG（X） is eit...For a finite group G, let S（G） be the set of minimal subgroups of odd order,which are complemented in G. It is proved that if every minimal subgroup X of odd orderof G which does not belong to S（G）, CG（X） is either subnormal or abnormal in G. Then Gsolvable.展开更多
Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate ...Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained.展开更多
A finite group G is called an J N J-group if every proper subgroup H of G is either subnormal in G or self-normalizing. We determinate the structure of non-J N J-groups in which all proper subgroups are J N J- groups.
基金supported by National Natural Science Foundation of China(Grant Nos.11501235,11601225,11171243)Natural Science Foundation of Jiangsu Province(No.BK20140451).
文摘Let G be a group and G=G_(1)G_(2) where G_(i) are subgroups of G.In this paper,we investigate the structure of G under the conditions that some subgroups of G_(i) are subnormal in G.
基金Supported by SRFPYED(2017ZDX041)and SRFPYED(2016ZDX151)
文摘In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
基金supported by the project of NSF of China(Grant No.12071092)the major project of Basic and Applied Research(Natural Science)in Guangdong Province,China(Grant No.2017KZDXM058)the Science and Technology Program of Guangzhou Municipality,China(Grant No.201804010088)。
文摘Denote the class of finite groups that are the product of two normal supersoluble subgroups and the class of groups that are the product of two subnormal supersoluble subgroups by B_(1)and B_(2),respectively.In this paper,a characterisation of groups in B_(1)or in B_(2)is given.By applying this new characterisation,some new properties of B_(1)(B_(2))and new proofs of many known results about B_(1)or B_(2)are obtained.Further,closure properties of B_(1)and B_(2)are discussed.
基金Supported by NSF of China(Grant Nos.10961007,10871210)NSF of Guangxi(Grant No.0991101)Guangxi Education Department
文摘Based on Wielandt＇s criterion for subnormality of subgroups in finite groups, we study 2-maximal subgroups of finite groups and present another subnormality criterion in finite solvable groups.
基金Supported by the Natural Science Foundation of Guangxi Autonomous Region（0249001）
文摘For a finite group G, let S（G） be the set of minimal subgroups of odd order,which are complemented in G. It is proved that if every minimal subgroup X of odd orderof G which does not belong to S（G）, CG（X） is either subnormal or abnormal in G. Then Gsolvable.
基金supported by National Natural Science Foundation of China (Grant Nos. 10771172, 10771180)
文摘Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained.
文摘A finite group G is called an J N J-group if every proper subgroup H of G is either subnormal in G or self-normalizing. We determinate the structure of non-J N J-groups in which all proper subgroups are J N J- groups.
