Fuzzy Subgroups of Rank Two Abelian p-Group

Document Type: Research Paper

Authors

1 Department of Mathematics (P&A), University of Fort Hare, Alice, 5700, South Africa

2 Department of Mathematics (P&A), Rhodes University, Grahamstown, 6140, South Africa

3 B. B. Makamba, Department of Mathematics (P&A), University of Fort Hare, Alice, 5700, South Africa

Abstract

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the subgroups of maximal chains in a special way which enables us to count the number of fuzzy subgroups.

Keywords


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