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
We obtain some sufficient conditions on the number of non-（sub）normai nonabelian subgroups of a finite group to be solvable, which extend a result of Shi and Zhang in 2011.
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.
文摘We obtain some sufficient conditions on the number of non-（sub）normai nonabelian subgroups of a finite group to be solvable, which extend a result of Shi and Zhang in 2011.
基金Research supported by the National Natural Science Foundation of China(11071229)the Natural Science Foundation for Colleges and Universities of Jiangsu Province(10KJD110004)the Postgraduate Innovation Grant of Xuzhou Normal University(2011YLB025)
