Investigation on Lesser Prime Order Subloops of Odd Order Moufang Loops | Asian Journal of Pure and

If L is a moufang loop of odd order p m, where p is the lowest prime, splitting |L| with (p,m)=1 and 1,2 is shown by Ademola and Rajah. Then there is a Lm normal subloop of order m in L. The existence of a normal subloop for a Moufang loop of any odd order is investigated in this work, with the requirement that every suitable subloop and quotient loop of L is a group. This is accomplished by evaluating a subloop L1 of order p q, where p and q are odd primes with 3pq, q 1(mod p), Z+, and 1 2 and looking into the possibility of a normal p - subloop of order p in L1.

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