Title of article :
On the commutativity degree in finite Moufang loops
Author/Authors :
Ahmadidelir ، Karim - Islamic Azad University, Tabriz Branch
Pages :
11
From page :
37
To page :
47
Abstract :
‎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.
Keywords :
Loop theory , Finite Moufang loops , Commutativity degree in finite groups
Journal title :
International Journal of Group Theory
Serial Year :
2016
Journal title :
International Journal of Group Theory
Record number :
2449065
Link To Document :
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