Masiwa, Thomas (2008) Some Aspects of Products of Totally Permutable Groups. MPhil thesis, University of Zimbabwe.
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Abstract
In this work groups factorised as products of pairwise totally permutable subgroups are investigated in the framework of SC-groups, PST-groups, PT-groups and T-groups. In particular an attempt is made to answer the following questions: Let G = G1G2 · · ·Gr be a product of pairwise totally permutable subgroups. If G is a T-group, under what conditions is Gi a T-group, for each i 2 {1, 2, · · · r}? Let G = G1G2 · · ·Gr be a product of pairwise totally permutable T-groups. Under what conditions is G a T-group? Similar questions are raised for PT-groups, PST-groups and SC-groups. It turns out that pairwise totally permutable factors are T-groups whenever the product is a T-group. Similar results hold for PT-groups, PST-groups and SC-groups. The product of pairwise totally permutable SC-groups is also an SC-group. However the direct product of PST-groups need not be a PST-group. If G = G1G2 · · ·Gr is the direct product of soluble PST-groups with |Gi| and |Gj | co-prime for all i, j 2 {1, 2, · · · , r} with i 6= j, then G is a PST-group.
| Item Type: | Thesis (MPhil) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Africana |
| Depositing User: | Geoffrey Obatsa |
| Date Deposited: | 03 May 2018 13:47 |
| Last Modified: | 03 May 2018 13:48 |
| URI: | http://thesisbank.jhia.ac.ke/id/eprint/3948 |
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