Groups satisfying the double chain condition on non-subnormal subgroups

Abstract

Abstract If θ is a subgroup property, a group G is said to satisfy the double chain condition on θ-subgroups if it admits no infinite double sequences ⋯ < X - n < ⋯ < X - 1 < X 0 < X 1 < ⋯ < X n < ⋯ \cdots<X_{-n}<\cdots<X_{-1}<X_{0}<X_{1}<\cdots<X_{n}<\cdots consisting of θ-subgroups. The structure of generalised radical groups satisfying the double chain condition on non-subnormal subgroups is described.