Constructing R-sequencings and terraces for groups of even order
The problem of finding R-sequencings for abelian groups of even orders has been reduced to that of finding R\(^*\)-sequencings for abelian groups of odd orders except in the case when the Sylow 2-subgroup is a non-cyclic non-elementary-abelian group of order~8. We partially address this exception,...
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| Date: | 2016 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2016
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/81 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | The problem of finding R-sequencings for abelian groups of even orders has been reduced to that of finding R\(^*\)-sequencings for abelian groups of odd orders except in the case when the Sylow 2-subgroup is a non-cyclic non-elementary-abelian group of order~8. We partially address this exception, including all instances when the group has order \(8t\) for \(t\) congruent to 1, 2, 3 or 4 \((\mod{7})\). As much is known about which odd-order abelian groups are R\(^*\)-sequenceable, we have constructions of R-sequencings for many new families of abelian groups. The construction is generalisable in several directions, leading to a wide array of new R-sequenceable and terraceable non-abelian groups of even order. |
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