Counting the number of fuzzy subgroups of an abelian group of order pnqm

✍ Scribed by V. Murali; B.B. Makamba

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 258 KB
• Volume: 144
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(03)00224-0

✦ Synopsis

In this paper, we determine the number of fuzzy subgroups of G = Z p n + Z q m where p; q are distinct primes, and n; m are any two natural numbers. First, we represent the number of maximal chains of G as a summation through m involving certain binomial coe cients. Using this concise expression, we propose a combinatorial formula for the number of fuzzy subgroups of G and verify it for speciÿc values of m and n. Finally, we sketch a proof for the general case.