Fuzzy Subgroups of Rank Two Abelian p-Group
نویسندگان
1 B. B. Makamba, Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa
2 Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa
3 Department of Mathematics (P\&A), Rhodes University, Grahamstown, 6140, South Africa
doi
10.22111/ijfs.2010.183چکیده
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.
