in this paper, we study fuzzy substructures in connection withhv-structures. the original idea comes from geometry, especially from thetwo dimensional euclidean vector space. using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. we connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as hv-groups...

in this paper, we verify the solvability of free product of finite cyclic groups with topological methods. we use cayley graphs and everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. in particular, using these methods, we prove that the commutator subgroup of $mathbb{z}_{m}*mathbb{z}_{n}$ is free of rank $(m-1)(n-1)$ fo...

a k-nacci sequence in a finite group is a sequence of group elements x0 , x1, x2 ,, xn , forwhich, given an initial (seed) set 0 1 2 1 , , , ,j x x x x  , each element is defined by0 1 11 1for ,for .nnn k n k nxx x j n kxx x x n k        in this paper, we examine the periods of the k-nacci sequences in miller’s generalization of the polyhedralgroups 2,2 2;q , n,2 2;q , 2, n 2;...

‎let $g$ be a group and $a=aut(g)$ be the group of automorphisms of‎ ‎$g$‎. ‎then the element $[g,alpha]=g^{-1}alpha(g)$ is an‎ ‎autocommutator of $gin g$ and $alphain a$‎. ‎also‎, ‎the‎ autocommutator subgroup of g is defined to be‎ ‎$k(g)=langle[g,alpha]|gin g‎, ‎alphain arangle$‎, ‎which is a‎ ‎characteristic subgroup of $g$ containing the derived subgroup‎ ‎$g'$ of $g$‎. ‎a group is defined...

a recursive-circulant $g(n; d)$ is defined to be acirculant graph with $n$ vertices and jumps of powers of $d$.$g(n; d)$ is vertex-transitive, and has some strong hamiltonianproperties. $g(n; d)$ has a recursive structure when $n = cd^m$,$1 leq c < d $ [10]. in this paper, we will find the automorphismgroup of some classes of recursive-circulant graphs. in particular, wewill find that the autom...

in this paper we find systems of subgroups of a finite‎ ‎group‎, ‎which $bbb p$-subnormality guarantees supersolvability‎ ‎of the whole group‎.

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

we introduce a two generated weakly branch contracting automaton group $g$ which is generated by a two state automaton on a three letter alphabet. using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. furthermore some algebraic properties of $g$ are detected .

‎given an integer $n$‎, ‎we denote by $mathfrak b_n$ and $mathfrak c_n$ the classes of all groups $g$ for which the map $phi_{n}:gmapsto g^n$ is a monomorphism and an epimorphism of $g$‎, ‎respectively‎. ‎in this paper we give a characterization for groups in $mathfrak b_n$ and for groups in $mathfrak c_n$‎. ‎we also obtain an arithmetic description of the set of all integers $n$ such that a gr...