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Random Walks on Finite Groups     Finite Groups  Random       2015/8/26
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 shuffling methods. ...
We study the rate of convergence of symmetric random walks on finite groups to the uniform distribution. A notion of moderate growth is introduced that combines with eigenvalue techniques to give sh...
MODERATE GROWTH AND RANDOM WALK ON FINITE GROUPS.
Markov chains on nite 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...
Let $R$ be a subset of a group $G$. We call a subgroup $H$ of $G$ the $R$-conjugate-permutable subgroup of $G$, if $HH^{x}=H^{x}H$ for all $x\in R$. This concept is a generalization of conjugate-permu...
Let $\C$ be a variety of finite groups. We use profinite Bass--Serre theory to show that if $u:H\hookrightarrow G$ is a map of finitely generated residually $\C$ groups such that the induced map $\hat...
Abstract: In the context of group-theoretic fast matrix multiplication the TPP capacity is used to bound the exponent $\omega$ of matrix multiplication. We prove a new and sharper upper bound for the ...
Abstract: In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with...
Abstract: In this paper we prove characterizations of $p$-nilpotency for fusion systems and $p$-local finite groups that are inspired by results in the literature for finite groups. In particular, we ...
Abstract: These are the notes from an Oberwolfach Seminar which we ran from 23--29 May 2010.
Abstract: Let $G$ be a finite group of Lie type and $\ell$ be a prime which is not equal to the defining characteristic of $G$. In this note we discuss some open problems concerning the $\ell$-modular...
The following result is proved. Let w be a multilinear commutator and n a positive integer. Suppose that G is a resid-ually finite group in which every product of at most 896 w-values has order divid...
We call a group G algorithmically finite if no algorithm can produce an infinite set of pairwise distinct elements of G. We construct examples of recursively presented infinite algorithmically finite...
In this paper we present some inequalities for the order, the expo-nent and the number of generators of the c-nilpotent multiplier (the Baer invariant with respect to the variety of nilpotent groups o...
We show that any faithful quasi-free actions of a finite group on the Cuntz algebra O1 are mutually conjugate, and that they are asymptotically rep-resentable.

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