radical group 20E15 4 2019 2 20F99 2 Hirsch-Zaitsev rank 2 Soluble group 2 chain conditions 2 factorized group 2 generalized radical group 2 locally nilpotent group 2 minimax group 2 minimax rank 2 non finitely generated subgroups 2 pronormal subgroup 2 soluble group 2 splitting theorems 2 stable soluble group 2 transitively normal subgroup 2 weak chain conditions 2 20E34 1 20F19 1 20F19,20F22 1 abnormal subgroups 1 contranormal subgroup 1 locally graded group 1 locally nilpotent group,transitively normal subgroup 1 non finitely generated subgroup 1 normal subgroups 1 permutable subgroups 1 pronormal subgroups 1