Enumerating AG-Groups with a Study of Smaradache AG-Groups
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Gretton, Charles
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Abstract
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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International Mathematical Forum
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6
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62
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© 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.
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Artificial Intelligence and Image Processing not elsewhere classified
Mathematical Sciences