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on the commutativity degree in finite moufang loops
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نویسنده
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ahmadidelir karim
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منبع
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international journal of group theory - 2016 - دوره : 5 - شماره : 3 - صفحه:37 -47
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چکیده
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the commutativity degree, , of a finite group g>g (i.e. the probability that two (randomly chosen) elements of g>gcommute with respect to its operation)) has been studied well by many authors. it is well-known that the best upper bound for pr(g)>pr(g) is 58>58 for a finite non-abelian group g>g. in this paper, we will define the same concept for a finite non--abelian moufang loop m>m and try to give a best upper bound for pr(m)>pr(m). we will prove that for a well-known class of finite moufang loops, named chein loops, and its modifications, this best upper bound is 2332>2332. so, our conjecture is that for any finite moufang loop m>m, pr(m)≤2332>pr(m)≤2332.
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کلیدواژه
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loop theory ,finite moufang loops ,commutativity degree in finite groups
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آدرس
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islamic azad university, tabriz branch, department of mathematics, ایران
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پست الکترونیکی
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kdelir@gmail.com, k ahmadi@iaut.ac.ir
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Authors
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