radical group 4 20E15 3 20F19 2 pronormal subgroup 2 soluble group 2 (generalized) radical group 1 2019 1 20E34 1 20F16 1 20F18 1 20F19,20F22 1 20F22 1 20F99 1 Hirsch-Zaitsev rank 1 Soluble group 1 \(GNA\)-subgroup 1 abnormal subgroup 1 abnormal subgroups 1 chain conditions 1 contranormal subgroup 1 factorized group 1 generalized radical group 1 locally finite radical 1 locally graded group 1 locally nilpotent group 1 locally nilpotent group,transitively normal subgroup 1 locally nilpotent radical 1 minimax group 1 minimax rank 1 non finitely generated subgroup 1