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Showing 1 to 5 of 5 for “"Moufang loops"”.
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Topics in Moufang Loops
<p>We will begin by discussing power graphs of Moufang loops. We are able to show that as in groups the directed power graph of a Moufang loop is uniquely determined by the undirected power graph. In the process of proving this result we define the generalized octonion loops, a variety of Moufang …
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The Near Normality of the Commutant of a Moufang Loop
… conditions under which the commutant of a Moufang loop is normal and related topics. We begin by giving relevant background on Moufang loops and normality. We then prove a theorem showing how close the commutant is to being normal: cR(x, y)R(x, y)R(x, y) = c. We then prove a couple of …
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On Loop Commutators, Quaternionic Automorphic Loops, and Related Topics
… definition of the commutator inside of loops. Moreover, we show that the commutator can be characterized by the generators of the inner mapping group of the loop. We then translate these results to characterize the commutator of two normal subloops of any loop.</p> <p>Second, we study …
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Zorn vector matrices over commutative rings and the loops arising from their construction
… Paige used to construct simple nonassociative Moufang loops over finite fields can, in fact, be done over any commutative ring with the proper adjustments. The resulting loops are still Moufang, but no longer simple in general. Given a commutative ring and an ideal of that ring, the loop …
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Sedenion extension loops and frames of hypercomplex 2[superscript n]-ons
… Although the sedenions do not directly yield loops in the way that Moufang loops are obtained from octonions, the left loop of non-zero sedenions does contain new two-sided subloops as sedenion extensions. These loops are constructed abstractly as extensions of subloops L of the octonions. The …