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

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    Author(s)
    Shah, Muhammad
    Gretton, Charles
    Griffith University Author(s)
    Gretton, Charles
    Year published
    2011
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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.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
    Publisher URI
    http://m-hikari.com/imf-2011/61-64-2011/shahmIMF61-64-2011.pdf
    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
    Publication URI
    http://hdl.handle.net/10072/46994
    Collection
    • Journal articles

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