20E28 3 20E32 3 20E34 3 20E32; 20E08 1 20F50 1 37A15 1 Hall subgroup 1 Schmidt subgroup 1 cofactors 1 derived subgroup 1 diagonal embeddings 1 direct limits 1 finite group 1 finite soluble group 1 insoluble groups 1 locally finite simple groups 1 maximal subgroups 1 measure-preserving actions 1 nilpotent subgroup 1 normal subgroup 1 semi-normal subgroup 1 soluble groups 1 subnormal subgroup 1