Babington Makamba
Department of Mathematics, University of Fort Hare, Alice 5700 , Eastern Cape , South Africa
[ 1 ] - Distinct Fuzzy Subgroups of a Dihedral Group of Order $2pqrs$ for Distinct Primes $p, , q, , r$ and $s$
In this paper we classify fuzzy subgroups of the dihedral group $D_{pqrs}$ for distinct primes $p$, $q$, $r$ and $s$. This follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.We present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...
[ 2 ] - The Remak-Krull-Schmidt Theorem on\ Fuzzy Groups
In this paper we study a representation of a fuzzy subgroup $mu$ of a group $G$, as a product of indecomposable fuzzy subgroups called the components of $mu$. This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and som...
[ 3 ] - Fuzzy Subgroups of Rank Two Abelian p-Group
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 s...
نویسندگان همکار