الفهرس | Only 14 pages are availabe for public view |
Abstract A maximal chain in a finite lattice L is called smooth if any two intervals of the same length are isomorphic. A finite group G is called TS-group (totally smooth group) if all its maximal chains in its subgroup lattice are smooth, and called GS-group (generalized smooth group) if [G/N] is totally smooth for every subgroup N of G of prime order. As a continuation to the study of smooth groups, this thesis is devoted to study some aspects of the theory of smooth groups. In this thesis we study the structure of a finite group G if: (1) All maximal subgroups of G are GS-groups and G has a subgroup H such that all maximal subgroups (or all minimal subgroups) of H are S-permutable in G. (2) M{p} is a TS-set and G has a subgroup H such that every maximal subgroup of H is S-permutable in G, where M{p} is the set of all maximal subgroups of G whose orders are divided by a prime p. Keywords: Smooth groups, totally smooth groups, generalized smooth groups, and S-permutable subgroups. |