Abstract

DETERMINING NILPOTENCY CLASS OF LOOPS OF SMALL ORDER

1 Okhuonurie. M?, 2Isere A. O. 3Aashikpelokhae U.S.U.

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Abstract The normality, the center and the derived notion of central nilpotency are important concepts in loops. Determining nilpotency class of loops of small orders is the main focus of this paper. Examples of some constructed commutative and non-commutative loops are shown. In order to determine the nilpotency class of the constructed loops using subnormal series method, we obtain the nuclei of the loops, the nucleus, the centrum, the center, the left and right cosets, the quotient set (factor loop), normal and proper subloops. Using subnormal series method, the nilpotency class of such loops were obtained and presented. A brief characterization of the constructed commutative loops of order 12 and of order 16 were obtained and presented. Keywords: Centrally nilpotent, Nilpotency class, Normal subloop, Proper subloop, Center of Quotient set, Subnormal series.

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