Related papers: Groups with special presentations and star-graph $…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

The contact graph of a packing of translates of a convex body in Euclidean $d$-space $\mathbb E^d$ is the simple graph whose vertices are the members of the packing, and whose two vertices are connected by an edge if the two members touch…

Let $G$ be a group and $Z(G)$ be its center. We associate a commuting graph ${\Gamma}(G)$, whose vertex set is $G\setminus Z(G)$ and two distinct vertices are adjacent if they commute. We say that ${\Gamma}(G)$ is strong $k$ star free if…

In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions $C'(1/6)$ and $C'(1/4)-T(4)$ has the property that the set of all geodesics (over the same generating set) is a…

Let $G= (V,E)$ be a finite graph. For $d_0>0$ we say that $G$ is $d_0$-regular, if every $v\in V$ has degree $d_0$. We say that $G$ is $(d_0, d_1)$-regular, for $0<d_1<d_0$, if $G$ is $d_0$ regular and for every $v\in V$, the subgraph…

In this work, we systematically derive explicit expressions for the Poincar\'e Group generators on arbitrary-rank tensors and spinor-tensors in $D=3+1$ and $D=2+1$ spacetimes, thus generalizing previous works in the literature for the…

We find strictly ascending HNN extensions of finite rank free groups possessing a presentation 2-complex which is a non positively curved square complex. On showing these groups are word hyperbolic, we have by results of Wise and Agol that…

We consider here 6-regular plane graphs whose faces have size 1, 2 or 3. In Section 2 a practical enumeration method is given that allowed us to enumerate them up to 53 vertices. Subsequently, in Section 3 we enumerate all possible symmetry…

We introduce the factorization graph of a finite group and study its connectedness and forbidden structures. We characterize all finite groups with connected factorization graphs and classify those with connected bipartite factorization…

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

Let $[n]^{(k)}$ be the set of all ordered $k$-tuples of distinct elements in $[n]=\{1,2,...,n\}$. The $(n,k,r)$-arrangement graph $A(n,k,r)$ with $1\leq r\leq k\leq n$, is the graph with vertex set $[n]^{(k)}$ and with two $k$-tuples are…

Let $X$ be a smooth quasi-projective variety. Assume that the (topological) fundamental group $\pi_1(X, x)$ is torsion-free nilpotent. We show that if the first Betti number $b_1(X) \le 3$, then $\pi_1(X, x)$ is isomorphic to either…

We give a necessary and sufficient condition for the fundamental group of a finite graph of groups with infinite cyclic edge groups to be acylindrically hyperbolic, from which it follows that a finitely generated group splitting over Z…

We introduce \emph{k-positive representations}, a large class of $\{1,\ldots,k\}$--Anosov surface group representations into PGL(E) that share many features with Hitchin representations, and we study their degenerations: unless they are…

The classification of elliptic curves E over the rationals Q is studied according to their torsion subgroups E_{tors}(Q) of rational points. Explicit criteria for the classification are given when E_{tors}(Q) are cyclic groups with even…

Suppose $G$ is a $\mathcal{T}$-group (finitely generated torsion-free nilpotent) with centralizers outside of the derived subgroup being abelian of rank equal to $\text{rank}(Z_1)+1$. This includes the class of free nilpotent groups…

We study analytic properties of graph product of finite groups with a hyperbolic defining graph. This is done by studying dynamics on the Bowditch compactification of the extension graph, or the crossing graph, of graph product. In…

By a result of Babai, with finitely many exceptions, every group $G$ admits a semi-regular poset representation with three orbits, that is, a poset $P$ with automorphism group $\textrm{Aut}(P) \simeq G$ such that the action of…

A graph product kernel means the kernel of the natural surjection from a graph product to the corresponding direct product. We prove that a graph product kernel of countable groups is special, and a graph product of finite or cyclic groups…

An irreducible representation of the free group on two generators X,Y into SL(2,C) is determined up to conjugation by the traces of X,Y and XY. We study the diagonal slice of representations for which X,Y and XY have equal trace. Using the…