this paper, deals with some equivalence relations in fuzzy subgroups. further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

A basis of quasi-invariant module over invariants is explicitly constructed for the two-dimensional Coxeter systems with arbitrary multiplicities. It is proved that this basis consists of m-harmonic polynomials, thus the earlier results of Veselov and the author for the case of constant multiplicity are generalized.

The structure of the title compound, C(19)H(17)BrN(2)O(3), consists of two cyclic groups, viz. 4-(meth-oxy-carbon-yl)phenyl and 6-(4-bromo-phen-yl)-3-oxo-2,3,4,5-dihydro-pyridazin-4-yl, which are linked by a methyl-ene spacer. The pyridazine ring is twisted and the dihedral angle between its mean plane and that of the bromo-phenyl mean plane is 17.2 (2)°. The 4-(meth-oxy-carbon-yl)phenyl group ...

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...