Generalizing Baer's norm (Q1755299)

Let \(G\) be a group and \(n\) a positive integer. The authors define \(B_n(G)\) to be the intersection of the normalizers of all the non-\(n\)-subnormal subgroups of \(G\). They give a new characterization for nilpotent groups in terms of a series defined via \(B_n(G)\). The authors also prove the following interesting result: Theorem 1.1. If \(G\) is a finite group and \(n\) is a positive integer, then there is a positive integer \(m\) so that \(B_n(G)\) is contained in \(Z_m(G)\) (the \(n\)-th term of the upper central series).