an:06114995
Zbl 1255.20021
Guo, Wenbin; Lu, Yi; Niu, Wenjuan
\(S\)-embedded subgroups of finite groups
EN
Algebra Logic 49, No. 4, 293-304 (2010); translation from Algebra Logika 49, No. 4, 433-450 (2010).
00271100
2010
j
20D40 20D20 20D10 20D25
finite groups; permutable subgroups; \(S\)-embedded subgroups; supersoluble groups; \(p\)-nilpotent groups; Sylow subgroups; quasinormal subgroups
Summary: A subgroup \(H\) of \(G\) is said to be \(S\)-embedded in \(G\) if \(G\) has a normal subgroup \(N\) such that \(HN\) is \(s\)-permutable in \(G\) and \(H\cap N\leqslant H_{sG}\), where \(H_{sG}\) is the largest \(s\)-permutable subgroup of \(G\) contained in \(H\). \(S\)-embedded subgroups are used to give novel characterizations for some classes of groups. New results are obtained and a number of previously known ones are generalized.