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...

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...

Many patients with frontotemporal dementia (FTD) have impaired sentence comprehension. However, the pattern of comprehension difficulty appears to vary depending on the clinical subgroup. The purpose of this study was to elucidate the neural basis for these deficits in FTD. We studied patients with two different presentations: Three patients with Progressive Non-Fluent Ahasia (PNFA), and five n...

In this paper, the notions of   , q  -Q-fuzzy subgroup and normal subgroup are introduced and some of their properties are investigated.

The theory of fuzzy sets was inspired by Zadeh [10]. Subsequently, Rosenfeld introduced the concept of a fuzzy subgroup of a group [9]. Fuzzy cosets and fuzzy normal subgroups of a group G have been studied in [3, 5, 8]. In [4], the ring of cosets of a fuzzy ideal was constructed. Let A and B be fuzzy subgroups of G such that B ⊆ A. The purpose of this paper is to introduce the notion of fuzzy ...

The singular braids with n strands, n≥3, were introduced independently by Baez and Birman. It is known that the monoid formed embedded in a group as braid group, denoted SGn. There has been another generalization of groups, GVBn, which was Fang symmetries behind quantum quasi-shuffle structures. GVBn simultaneously generalizes classical well virtual on strands.We investigate commutator subgroup...

In this paper we classify fuzzy subgroups of a rank-3 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:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

We prove that a parabolic subgroup P P contained in another P prime"> ′ encoding="application/x...