Splitting in finite metacyclic groups
| dc.contributor.advisor | Grove, Larry C. | en_US |
| dc.contributor.author | Jackson, Jack Lee | |
| dc.creator | Jackson, Jack Lee | en_US |
| dc.date.accessioned | 2013-05-09T09:25:31Z | |
| dc.date.available | 2013-05-09T09:25:31Z | |
| dc.date.issued | 1999 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10150/289018 | |
| dc.description.abstract | It is well known that all finite metacyclic groups have a presentation of the form G = ‹a,x,aᵐ = 1,xˢaᵗ = 1,aˣ = aʳ›. The primary question that occupies this dissertation is determining under what conditions a group with such a presentation splits over the given normal subgroup ‹a›. Necessary and sufficient conditions are given for splitting, and techniques for finding complements are given in the cases where G splits over ‹a›. Several representative examples are examined in detail, and the splitting theorem is applied to give alternate proofs of theorems of Dedekind and Blackburn. | |
| dc.language.iso | en_US | en_US |
| dc.publisher | The University of Arizona. | en_US |
| dc.rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | Splitting in finite metacyclic groups | en_US |
| dc.type | text | en_US |
| dc.type | Dissertation-Reproduction (electronic) | en_US |
| thesis.degree.grantor | University of Arizona | en_US |
| thesis.degree.level | doctoral | en_US |
| dc.identifier.proquest | 9946817 | en_US |
| thesis.degree.discipline | Graduate College | en_US |
| thesis.degree.discipline | Mathematics | en_US |
| thesis.degree.name | Ph.D. | en_US |
| dc.identifier.bibrecord | .b39915323 | en_US |
| refterms.dateFOA | 2018-08-16T04:02:24Z | |
| html.description.abstract | It is well known that all finite metacyclic groups have a presentation of the form G = ‹a,x,aᵐ = 1,xˢaᵗ = 1,aˣ = aʳ›. The primary question that occupies this dissertation is determining under what conditions a group with such a presentation splits over the given normal subgroup ‹a›. Necessary and sufficient conditions are given for splitting, and techniques for finding complements are given in the cases where G splits over ‹a›. Several representative examples are examined in detail, and the splitting theorem is applied to give alternate proofs of theorems of Dedekind and Blackburn. |
