Related papers: Any strongly controllable group system or group sh…

With each piecewise monotonic map of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t^{-1}] module, is finitely generated, and generators are identified. Dimension groups are computed for Markov…

For every countable group G we construct a compact path connected subspace K of R^4 whose fundamental group is isomorphic to G. Our construction is much simpler than the one found recently by Virk.

We consider linear groups which do not contain unipotent elements of infinite order, which includes all linear groups in positive characteristic, and show that this class of groups has good properties which resemble those held by groups of…

An extension of the Lorentz group to include generators $\Gamma^\mu$ carrying a space-time index is demonstrated to explicitly construct the Minkowski metric within the internal group space as a consequence of the non-vanishing commutation…

An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of these is a finite abelian group known as its critical group.…

In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $G$ is said to admit a uniform group factorization if there…

For a tropical curve and a finite subgroup of the isometry group of the tropical curve, we prove, extending the work by Haase, Musiker and Yu, that the invariant part of the complete linear system associated to a invariant effective divisor…

Batch codes serve as critical tools for load balancing in distributed storage systems. While numerous constructions exist for specific batch sizes t, current methodologies predominantly rely on code dimension parameters, limiting their…

In this paper, we investigate the computational complexity of isomorphism testing for finite groups and quasigroups, given by their multiplication tables. We crucially take advantage of their various decompositions to show the following: -…

Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…

Let $G$ be a finite $2$-generated non-cyclic group. The spread of $G$ is the largest integer $k$ such that for any nontrivial elements $x_1, \ldots, x_k$, there exists $y \in G$ such that $G = \langle x_i, y\rangle$ for all $i$. The more…

This paper considers generators of Heisenberg modules in the case of twisted group $C^*$-algebras of closed subgroups of locally compact abelian groups and how the restrction and/or periodization of these generators yield generators for…

The expressibility and trainability of parameterized quantum circuits has been shown to be intimately related to their associated dynamical Lie algebras (DLAs). From a quantum algorithm design perspective, given a set $A$ of DLA generators,…

Let $G$ be a countable group, $\operatorname{Sub}(G)$ the (compact, metric) space of all subgroups of $G$ with the Chabauty topology and $\operatorname{Is}(G) \subset \operatorname{Sub}(G)$ the collection of isolated points. We denote by…

Let $A$ be a finite dimensional commutative associative algebra with unit over an algebraically closed field of characteristic zero. The group $G(A)$ of invertible elements is open in $A$ and thus $A$ has a structure of a prehomogeneous…

Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed exposition of 'degroupoidification': a…

The algebra of symmetric functions contains several interesting families of symmetric functions indexed by integer partitions or skew partitions. Given a sequence $\{u_n\}$ of symmetric functions taken from one of these families such that…

Let $R$ be a commutative ring with $\Z(R)$ its set of zero-divisors. In this paper, we study the total graph of $R$, denoted by $\T(\Gamma(R))$. It is the (undirected) graph with all elements of $R$ as vertices, and for distinct $x, y\in…

We determine the structure of finitely generated groups which are quasi-isometric to symmetric spaces of noncompact type, allowing Euclidean de Rham factors If $X$ is a symmetric space of noncompact type with no Euclidean de Rham factor,…

We introduce a new type of equivalence between blocks of finite group algebras called a strong isotypy. A strong isotypy is equivalent to a $p$-permutation equivalence and restricts to an isotypy in the sense of Brou\'{e}. To prove these…