Isaac K. Appiah - Department of Mathematics, University of Fort Hare, ALICE, ۵۷۰۰, South Africa
B. B. Makamba - Department of Mathematics, University of Fort Hare, ALICE, ۵۷۰۰, South Africa

In this paper we classify fuzzy subgroups of a rank-۳ abelian group G = \mathbb{Z}_{p^n} + \mathbb{Z}_p + \mathbb{Z}_p for any fixed prime p and any positive integer n, using a natural equivalence relation given in \cite{mur:۰۱}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorphic maximal chains of subgroups and (v) classes of isomorphic fuzzy subgroups of G. Illustrative examples are provided.

Equivalence, Fuzzy subgroup, Maximal chain, Keychain, Distinguishing factor, Isomorphism