Investigation on Lesser Prime Order Subloops of Odd Order Moufang Loops

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Published: 2021-11-03

Page: 79-82


Lois A. Ademola *

Department of Mathematics, University of Jos, Jos, Nigeria.

Garba G. Zaku

Department of Mathematics, University of Jos, Jos, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

Ademola and Rajah have proven that if L is a moufang loop of odd order pα m, where p is the smallest prime dividing |L| with (p,m)=1 and α∈{1,2}. Then there exists a subloop Lm of order m normal in L. This paper goes further to investigate the existence of a normal subloop for Moufang loop of any odd order, with the condition that every proper subloop and quotient loop of L is a group. This is done by considering a subloop L1 of order pα qβ where p and q are odd primes with 3<p<q, q ≢ ±1(mod p), α ∈Z+ and 1 ≤ β ≤ 2, and investigating the possible existence of a normal p - subloop of order pα in L1 .

Keywords: Moufang loop, order, prime, nonassociative, normal, subloops


How to Cite

Ademola, L. A., & Zaku, G. G. (2021). Investigation on Lesser Prime Order Subloops of Odd Order Moufang Loops. Asian Journal of Pure and Applied Mathematics, 3(1), 79–82. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1326

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