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   on the commutativity degree in finite moufang loops  
   
نویسنده ahmadidelir karim
منبع international journal of group theory - 2016 - دوره : 5 - شماره : 3 - صفحه:37 -47
چکیده    ‎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.
کلیدواژه loop theory ,finite moufang loops ,commutativity degree in finite groups
آدرس islamic azad university, tabriz branch, department of mathematics, ایران
پست الکترونیکی kdelir@gmail.com, k ahmadi@iaut.ac.ir
 
     
   
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