A Generalization of σ-Permutability  

作　　者：Zhigang Wang Jin Guo Inna N.Safonova Alexander N.Skiba 

机构地区：[1]School of Science,Hainan University,Haikou 570228,Hainan,People’s Republic of China [2]Department of Applied Mathematics and Computer Science,Belarusian State University,220030 Minsk,Belarus [3]Department of Mathematics and Technologies of Programming,Francisk Skorina Gomel State University,246019 Gomel,Belarus

出　　处：《Communications in Mathematics and Statistics》2022年第3期565-579,共15页数学与统计通讯（英文）

基　　金：supported by the NNSF of China(No.12171126,11961017);supported by Ministry of Education of the Republic of Belarus(grant 20211328);supported by the BRFFR(grant F20R-291).

摘　　要：Throughout this paper,all groups are finite and G always denotes a finite group;σis some partition of the set of all primes P.A group G is said to beσ-primary if G is aπ-group for someπ∈σ.Aπ-semiprojector of G[29]is a subgroup H of G such that HN/N is a maximalπ-subgroup of G/N for all normal subgroups N of G.LetП⊆σ.Then we say thatχ={X_(1),...,X_(t)}is aП-covering subgroup system for a subgroup H in G if all members of the setχareσ-primary subgroups of G and for eachπ∈Пwithπ∩π(H)≠φthere are an index i and aπ-semiprojector U of H such that U≤X_(i).We study the embedding properties of subgroups H of G under the hypothesis that G has aП-covering subgroup systemχsuch that H permutes with X^(x)for all X∈χand x∈G.Some well-known results are generalized.

关 键 词：Finite group σ-nilpotent group П-semiprojector П-covering subgroup system σ-subnormal subgroup 

分 类 号：O15[理学—数学]