Related papers: Homogeneous Groups and Covers

Let $X$ be a finite set such that $|X|=n$ and let $i\leq j \leq n$. A group $G\leq \sym$ is said to be $(i,j)$-homogeneous if for every $I,J\subseteq X$, such that $|I|=i$ and $|J|=j$, there exists $g\in G$ such that $Ig\subseteq J$.…

Let X be a finite CW complex. We show that the fundamental group of X is large if and only if there is a finite cover Y of X and a sequence of finite abelian covers \{Y_N\} of Y which satisfy b_1(Y_N)\geq N. We give some applications of…

This paper deals with some results concerning finitely generated coreduced comultiplication modules over a commutative ring.

We describe the second homotopy group of any CW-complex $K$ by analyzing the universal cover of a locally finite model of $K$ using the notion of $G$-coloring of a partially ordered set. As applications we prove a generalization of the…

This is the author's PhD thesis, as submitted to the Princeton University. The results of this paper have already appeared in arXiv:math/0607777v4, arXiv:math/0607691 and arXiv:0901.2156.

Relying on the computation of the Andre-Quillen homology groups for unstable Hopf algebras, we prove that the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra.

Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.

Let $G$ be a finite group and $k$ a field of characteristic $p$. We conjecture that if $M$ is a $kG$-module with $H^*(G,M)$ finitely generated as a module over $H^*(G,k)$ then as an element of the stable module category…

We show that in the category of groups, every singly-generated class which is closed under isomorphisms, direct limits and extensions is also singly-generated under isomorphisms and direct limits, and in particular is co-reflective. We also…

The dead-end depth of an element g of a group G, with respect to a generating set A is the distance from g to the complement of the radius $d_A(1,g)$ closed ball, in the word metric $d_A$ defined with respect to A. We exhibit a finitely…

This should be the final version of this paper. Numberous minor improvements have been made to the manuscript, one argument has been corrected, and an appendix has been added.

Teams are the fundamental units propelling innovation and advancing modern science. A rich literature links the fundamental features of teams, such as their size and diversity, to academic success. However, such analyses fail to capture…

The subgroup pattern of a finite group $G$ is the table of marks of $G$ together with a list of representatives of the conjugacy classes of subgroups of $G$. In this article we describe a collection of sequences realized by the subgroup…

The main goal of the paper is to prove the existence of the universal cover for $RCD^*(K,N)$-spaces. This generalizes earlier work of C. Sormani and the second named author on the existence of universal covers for Ricci limit spaces. As a…

Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.

This thesis is divided into two parts. In the first part, we study models of $(\infty,\omega)$-categories. The main result is to establish a Quillen equivalence between Rezk's complete Segal $\Theta$-spaces and Verity's complicial sets. In…

We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving…

This work results from a study of Nicholas Kuhn's paper entitled "Generic representation theory of finite fields in nondescribing characteristic". Our goal is to abstract the categorical structure required to obtain an equivalence between…

We classify the finite connected-homogeneous digraphs, as well as the infinite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.

We show that the kernel of the monodromy representation for hypersurfaces of degree d and dimension n is large for d at least three with the exception of the cases (d,n) = (3,0) and (3,1). For these the kernel is finite. By "large" we mean…