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Abstract
Let G be a finite group. Two subgroups H and K of G permute if HK = KH. The subgroups H and K of G are mutually permutable if H permutes with every subgroup of K and vice-versa. A subgroup H of G is S -permutable in G if it permutes with every Sylow subgroup of G. A PST-group is a group G whose subnormal subgroups are all S-permutable in G. We say that G is a PST0 -group if its Frattini quotient group is a PST -group, where O(G) denotes the Frattini
subgroup of G. The object of this thesis is to investigate the structure of finite groups that’are the mutually permutable products of two solvable PST -groups (solvable PSTQ -groups).