%0 Journal Article
%T Conjugate loops: an introduction
%A A. Batool
%A A. Shaheen
%A A. Ali
%J International Mathematical Forum
%D 2013
%I 
%X In general conjugate of an element does not have any sense in loops. Weintroduce a new class of loops that possess conjugates of their elements. We call such loops conjugate loops. Conjugate loops are loops in which the identity $x(yx^{-1})=(xy)x^{-1}$ holds. We prove that such loops satisfy begin{inparaenum}[(1)] item An IP loop is conjugate $iff$ it is flexible, item Conjugacy is not an equivalence relation in conjugate loops. We also prove several other related results for conjugate loops end{inparaenum}
%K conjugate loop
%K flexible IP loop
%K conjugate IP loop
%U http://www.m-hikari.com/imf/imf-2013/5-8-2013/aliIMF5-8-2013.pdf