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Showing 1 to 2 of 2 for “"multiplication groups"”.
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On Multiplication Groups of Quasigroups
<p>Quasigroups are algebraic structures in which divisibility is always defined. In this thesis we investigate quasigroups using a group-theoretic approach. We first construct a family of quasigroups which behave in a group-like fashion. We then focus on the multiplication groups of quasigroups, …
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Cayley-Dickson Loops
… We study the structure of the automorphism groups of <em>Q<sub>n</sub></em>. We show that all subloops of <em>Q<sub>n</sub></em> of order 16 fall into two isomorphism classes, in particular, any such subloop is either isomorphic to the octonion loop O<sub>16</sub>, or the quasioctonion loop …