Quasinormal subgroups of infinite groups.
It is well-known that if \(G\) is a finite group and \(H\) is a quasinormal subgroup of \(G\), that is, \(H\) satisfies \(HK=KH\) for every \(K\leq G\), then \(H\) is subnormal in \(G\), \(H/H_G\) is nilpotent, and it even is contained in the hypercentre of \(G/H_G\). It is also well-known that none of these three assertions is true for arbitrary groups. The author gives a survey (without proofs) of what is known to hold under suitable assumptions on \(G\) or \(H\).
scientific article; zbMATH DE number 6378245
scientific article