Add to ORKGA finite set W ⊂ Rd is said to realize the group G if the isometry group of W is isomorphic to G. The isometry dimension of a group is the minimum dimension of a real-ization. It is known that the isometry dimension of G is less than |G | [1]. We show that the isometry dimension of Zn2 is n. The orbit number of a group is the minimum number of orbits in a realization. We show that the groups Zn2 are the only abelian groups with orbit number 1. We provide examples that illuminate these parameters.
A well known classical theorem due to Bieberbach says that every discrete group Γ of isometries of t...
We prove that if H is a subgroup of index n of any cyclic group G then G can be isometrically embedd...
AbstractLet G be a group (or vector space) and A a group of transformations of G. A then acts as a g...
A finite set W ⊂ Rd is said to realize the group G if the isometry group of W is isomorphic to G. Th...
A set of points W in Euclidean space is said to realize the finite group G if the isometry group of ...
AbstractA set of points W in Euclidean space is said to realize the finite group G if the isometry g...
A graph X is said to represent the group G with k edge (vertex) orbits if the automorphism group of ...
AbstractFor a finite group G and a set I ⊆ {1, 2,…, n} let G(n,I) = ∑g ∈ G ε1(g)⊗ε2(g)⊗⋯⊗εn(g),where...
Group theory and its applications are relevant in many areas of mathematics. Our project considers f...
We can construct an edge colored complete graph of a group by generalizing the notion of distance in...
We investigate the relationship between various isomorphism invariants for finite groups. Specifical...
Informally, essential dimension is the minimal number of parameters required to define an algebraic ...
The group of diffeomorphisms of a compact manifold acts isometrically on the space of Riemannian met...
The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show tha...
Restrictions imposed on the topology of a space X by the action of a group G are investigated via an...
A well known classical theorem due to Bieberbach says that every discrete group Γ of isometries of t...
We prove that if H is a subgroup of index n of any cyclic group G then G can be isometrically embedd...
AbstractLet G be a group (or vector space) and A a group of transformations of G. A then acts as a g...
A finite set W ⊂ Rd is said to realize the group G if the isometry group of W is isomorphic to G. Th...
A set of points W in Euclidean space is said to realize the finite group G if the isometry group of ...
AbstractA set of points W in Euclidean space is said to realize the finite group G if the isometry g...
A graph X is said to represent the group G with k edge (vertex) orbits if the automorphism group of ...
AbstractFor a finite group G and a set I ⊆ {1, 2,…, n} let G(n,I) = ∑g ∈ G ε1(g)⊗ε2(g)⊗⋯⊗εn(g),where...
Group theory and its applications are relevant in many areas of mathematics. Our project considers f...
We can construct an edge colored complete graph of a group by generalizing the notion of distance in...
We investigate the relationship between various isomorphism invariants for finite groups. Specifical...
Informally, essential dimension is the minimal number of parameters required to define an algebraic ...
The group of diffeomorphisms of a compact manifold acts isometrically on the space of Riemannian met...
The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show tha...
Restrictions imposed on the topology of a space X by the action of a group G are investigated via an...
A well known classical theorem due to Bieberbach says that every discrete group Γ of isometries of t...
We prove that if H is a subgroup of index n of any cyclic group G then G can be isometrically embedd...
AbstractLet G be a group (or vector space) and A a group of transformations of G. A then acts as a g...