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Walks on generating sets of Abelian groups
Markov chains on finite sets are used in a great variety of situations to approximate, understand and sample from their limit distribution. A familiar example is provided by card shufflin...
We study a Markov chain on generating n-tuples of a ®xed group which arises in algorithms for manipulating ®nite groups. The main tools are comparison of two Markov chains on di€erent...
Supercharacter formulas for pattern groups
In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse B...
In this paper, the first of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs is an expander and the girth of the graphs tends to infin...
We provide a direct and elementary proof of the equivalence between the weak asymptotic homomorphism property for the pair of group von Neumann algebras $L(H)\subset L(G)$ and the embedding into $H$ ...
A packing of subsets $\mathcal S_1,..., \mathcal S_n$ in a group $G$ is a sequence $(g_1,...,g_n)$ such that $g_1\mathcal S_1,...,g_n\mathcal S_n$ are disjoint subsets of $G$. We give a formula for t...
A path in an edge-colored graph $G$, where adjacent edges may have the same color, is called a rainbow path if no two edges of the path are colored the same. The rainbow connectivity $rc(G)$ of $G$ i...
We prove that, for p an odd prime, every finite p-group of rank 3 acts freely on a finite complex X homotopy equivalent to a product of three spheres
We show that if G is a finite group then no chain of modular elements in its subgroup lattice L(G) is longer than a chief series. Also, we show that if G is a nonsolvable finite group then every maxi...
In this paper we explore the method of holomorphic induction for unitary representations of Banach--Lie groups. First we show that the classification of complex bundle structures on homogeneous Banac...
Our first theorem is a version of the five lemma in a certain situation of pointed sets arising from non-abelian 1-cohomology. For our second, we show that a connected, unipotent algebraic group Q ac...
In this paper we give an intimate connection between the characteristic zero representation theories of the Additive and Heisenberg groups, and their characteristic p >0 theories when p is much larger...

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