Related papers: Dimension and partial groups

The supremum of lengths of strict chains of nested centralizers is called the $c$-dimension (centralizer dimension) of $G$. We prove two structure theorems for locally finite groups of finite $c$-dimension. We also prove that the…

Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…

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…

Let $G$ be a finite group and $\phi\colon V\to W$ an equivariant morphism of finite dimensional $G$-modules. We say that $\phi$ is faithful if $G$ acts faithfully on $\phi(V)$. The covariant dimension of $G$ is the minimum of the dimension…

The strong global dimension of a ring is the supremum of the length of perfect complexes that are indecomposable in the derived category. In this note we characterize the noetherian commutative rings that have finite strong global…

The dimension of random simplicial complexes (defined as the maximal dimension among all faces) is a natural extreme value associated with the complex, and is closely related to other functionals defined by a maximum, such as the clique…

We compute the essential dimension of finite groups of order $\leqslant 63$.

We give a simple formula for the essential dimension of a finite pseudo-reflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the "poor man's essential…

We give examples of finite quantum permutation groups which arise from the twisting construction or as bicrossed products associated to exact factorizations in finite groups. We also give examples of finite quantum groups which are not…

We define a finite-dimensional partially formal supermanifold as a manifold having $q$ odd coordinates and $k + l$ even coordinates with $l$ of them taking only nilpotent values. We show that this notion can be used to formulate…

A space is defined to be "$n$-spheroidal" if it has the homotopy type of an $n$-dimensional CW-complex $X$ with $H_{n}(X, \mathbb{Z})$ not zero and finitely generated. A group $G$ is called "$n$-spheroidal" if its classifying space $K(G,1)$…

Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies the bound $|H|^3 \ge |G|$. In this note we determine all the large maximal subgroups of finite simple groups, and we establish an…

We define a notion of roundness for finite groups. Roughly speaking, a group is round if one can order its elements in a cycle in such a way that some natural summation operators map this cycle into new cycles containing all the elements of…

A numerical semigroup is an additive subsemigroup of the natural numbers that contains zero and has finite complement. A numerical semigroup is irreducible if it cannot be written as an intersection of numerical semigroups properly…

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any…

A dimension group is an ordered abelian group that is an inductive limit of a sequence of simplicial groups, and a stationary dimension group is such an inductive limit in which the homomorphism is the same at every stage. If a simple…

Based on recent successes concerning permutation resolutions of representations by Balmer and Gallauer we define a new invariant of finite groups: the p-permutation dimension. We define this analogously to the global dimension of a ring by…

We define the Peano dimension for groups arising as fundamental groups, which generalizes the classical definition of geometric dimension of finitely presented groups. We conjecture that the Peano dimension of the fundamental group of a…

The integral group rings $\mathbb{Z}G$ for finite groups $G$ are precisely those fusion rings whose basis elements have Frobenius-Perron dimension 1, and each is categorifiable in the sense that it arises as the Grothendieck ring of a…

We describe structure of locally finite groups of finite centraliser dimension.