According to Hall,a subgroup H of a group G is said to be pronormal if H and H^(g) are conjugate in<H,H^(g)>for every g∈G.In this survey,we discuss the role of pronormality for some subgroups of finite groups:H...According to Hall,a subgroup H of a group G is said to be pronormal if H and H^(g) are conjugate in<H,H^(g)>for every g∈G.In this survey,we discuss the role of pronormality for some subgroups of finite groups:Hall subgroups,subgroups of odd index,submaximal X-subgroup,etc.展开更多
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
Let X be a nonempty subset of a group G. A subgroup H of G is said to be X-spermutable in G if, for every Sylow subgroup T of G, there exists an element x E X such that HT^x= T^xH. In this paper, we obtain some result...Let X be a nonempty subset of a group G. A subgroup H of G is said to be X-spermutable in G if, for every Sylow subgroup T of G, there exists an element x E X such that HT^x= T^xH. In this paper, we obtain some results about the X-s-permutable subgroups and use them to determine the structure of some finite groups.展开更多
基金supported by a NNSF Grant of China(Grant#11771409)Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Sciencesby SB RAS Fundamental Research Program I.1.1(project#0314-2016-0001).
文摘According to Hall,a subgroup H of a group G is said to be pronormal if H and H^(g) are conjugate in<H,H^(g)>for every g∈G.In this survey,we discuss the role of pronormality for some subgroups of finite groups:Hall subgroups,subgroups of odd index,submaximal X-subgroup,etc.
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Foundation item： the National Natural Science Foundation of China （No. 10771180） the Postgraduate Innovation Grant of Jiangsu Province and the International Joint Research Fund between NSFC and RFBR.
文摘Let X be a nonempty subset of a group G. A subgroup H of G is said to be X-spermutable in G if, for every Sylow subgroup T of G, there exists an element x E X such that HT^x= T^xH. In this paper, we obtain some results about the X-s-permutable subgroups and use them to determine the structure of some finite groups.
