Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2019; 34(4): 1049-1067

Online first article August 27, 2019      Printed October 31, 2019

https://doi.org/10.4134/CKMS.c180341

Copyright © The Korean Mathematical Society.

Computing fuzzy subgroups of some special cyclic groups

Babington Makamba, Michael M. Munywoki

University of Fort Hare; Technical University of Mombasa

Abstract

In this paper, we discuss the number of distinct fuzzy subgroups of the group $\mathbb{Z}_{p^n}\times \mathbb{Z}_{q^m}\times \mathbb{Z}_r$, $m=1,2,3$ where $p,q,r$ are distinct primes for any $n\in \mathbb{Z}^+$ using the criss-cut method that was proposed by Murali and Makamba in their study of distinct fuzzy subgroups. The criss-cut method first establishes all the maximal chains of the subgroups of a group $G$ and then counts the distinct fuzzy subgroups contributed by each chain. In this paper, all the formulae for calculating the number of these distinct fuzzy subgroups are given in polynomial form.

Keywords: maximal chain, equivalence, fuzzy subgroups

MSC numbers: Primary 20N25, 03E72; Secondary 20K01, 20K27

Supported by: The second author would like to thank the NRF of South Africa for financial support towards the completion of this paper.