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arXiv · 1106.2981

AG-groups and other classes of right Bol quasigroups

Muhammad Shah·Sergey Shpectorov·Asif Ali
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Abstract

By a result of Sharma, right Bol quasigroups are obtainable from right Bol loops via an involutive automorphism. We prove that the class of AG-groups, introduced by Kamran, is obtained via the same construction from abelian groups. We further introduce a new class of Bol* quasigroups, which turns out to correspond, as above, to the class of groups. Sharma's correspondence allows an efficient implementation and we present some enumeration results for the above three classes.

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Muhammad Shah, Sergey Shpectorov, Asif Ali. 2011-06-21. AG-groups and other classes of right Bol quasigroups. https://arxiv.org/abs/1106.2981

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