COUNTING DISTINCT FUZZY SUBGROUPS OF SOME RANK-۳ ABELIAN GROUPS

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.

کلیدواژه ها:

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