Enumerating AG-Groups with a Study of Smaradache AG-Groups

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Author(s)
Shah, Muhammad
Gretton, Charles
Griffith University Author(s)
Year published
2011
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AG-groups are a generalisation of Abelian groups. They correspond to groupoids with a left identity, unique inverses, and satisfy the identity (xy)z = (zy)x. We present the first enumeration result for AG-groups up to order 11 and give a lower bound for order 12. The counting is performed with the finite domain enumerator FINDER using bespoke symmetry breaking techniques. We have also developed a function in the GAP computer algebra system to check the generated Cayley tables. This note discusses a few observations obtained from our results, some of which inspired us to examine and discuss Smaradache AG-group structures.AG-groups are a generalisation of Abelian groups. They correspond to groupoids with a left identity, unique inverses, and satisfy the identity (xy)z = (zy)x. We present the first enumeration result for AG-groups up to order 11 and give a lower bound for order 12. The counting is performed with the finite domain enumerator FINDER using bespoke symmetry breaking techniques. We have also developed a function in the GAP computer algebra system to check the generated Cayley tables. This note discusses a few observations obtained from our results, some of which inspired us to examine and discuss Smaradache AG-group structures.
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Journal Title
International Mathematical Forum
Volume
6
Issue
62
Copyright Statement
© The Author(s) 2011. This is an Open Access article distributed under the terms of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Subject
Artificial Intelligence and Image Processing not elsewhere classified
Mathematical Sciences