Splitting in finite metacyclic groups
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 su...
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The University of Arizona.
1999
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ndltd-arizona.edu-oai-arizona.openrepository.com-10150-2890182015-10-23T05:11:48Z Splitting in finite metacyclic groups Jackson, Jack Lee Grove, Larry C. Mathematics. 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. 1999 text Dissertation-Reproduction (electronic) http://hdl.handle.net/10150/289018 9946817 .b39915323 en_US 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. The University of Arizona. |
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NDLTD |
| language |
en_US |
| sources |
NDLTD |
| topic |
Mathematics. |
| spellingShingle |
Mathematics. Jackson, Jack Lee Splitting in finite metacyclic groups |
| description |
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. |
| author2 |
Grove, Larry C. |
| author_facet |
Grove, Larry C. Jackson, Jack Lee |
| author |
Jackson, Jack Lee |
| author_sort |
Jackson, Jack Lee |
| title |
Splitting in finite metacyclic groups |
| title_short |
Splitting in finite metacyclic groups |
| title_full |
Splitting in finite metacyclic groups |
| title_fullStr |
Splitting in finite metacyclic groups |
| title_full_unstemmed |
Splitting in finite metacyclic groups |
| title_sort |
splitting in finite metacyclic groups |
| publisher |
The University of Arizona. |
| publishDate |
1999 |
| url |
http://hdl.handle.net/10150/289018 |
| work_keys_str_mv |
AT jacksonjacklee splittinginfinitemetacyclicgroups |
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1718103952414736384 |