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Abstract: The complete list of pairs of non-isomorphic finite simple groups having the same order is well-known. In particular for p>3, PSL_2(Z/p) is the "only" simple group of order (p^3-p)/2. It's l...
Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups
Residually nilpotent group entropy of automorphisms of groups pseudo-Anosov dilatation
2011/9/15
Abstract: We study the word length entropy of automorphisms of residually nilpotent groups, and how the entropy of such group automorphisms relates to the entropy of induced automorphisms on various n...
Amalgamated Products of Groups II: Measures of Random Normal Forms
Amalgamated Products Measures of Random Normal Forms Group Theory
2011/9/15
Abstract: Let $G=\mathop{A\ast B}\limits_C$ be an amalgamated product of finite rank free groups $A$, $B$ and $C$. We introduce atomic measures and corresponding asymptotic densities on a set of norma...
Abstract: We study the Hirsch-Plotkin radical of stability groups of (general) subspace series of infinite dimensional vector spaces. We show that in countable dimension and some other cases, the HP-r...
Verbal subgroups of hyperbolic groups have infinite width
Verbal subgroups hyperbolic groups Group Theory
2011/9/14
Abstract: Let $G$ be a non-elementary hyperbolic group. Let $w$ be a group word such that the set $w[G]$ of all its values in $G$ does not coincide with $G$ or 1. We show that the width of verbal subg...
Groups acting simply transitively on hyperbolic buildings
Groups hyperbolic buildings Group Theory
2011/9/14
Abstract: We construct and classify all groups acting simply transitively on vertices of hyperbolic triangular buildings of the smallest non-trivial thickness. We have both torsion and torsion free gr...
Sieve methods in group theory I: Powers in Linear groups
Sieve Property-T Powers Linear groups Finite groups of Lie type
2011/9/14
Abstract: A general sieve method for groups is formulated. It enables one to "measure" subsets of a finitely generated group. As an application we show that if $\Gamma$ is a finitely generated non vir...
From automatic structures to automatic groups
automatic structures automatic groups Group Theory
2011/9/14
Abstract: In this paper we introduce the concept of a Cayley graph automatic group (CGA group or graph automatic group, for short) which generalizes the standard notion of an automatic group. Like the...
Abstract: Subsurface projection has become indispensable in studying the geometry of the mapping class group and the curve complex of a surface. When the subsurface is an annulus, this projection is s...
Waring Problem for Finite Quasisimple Groups
Finite Quasisimple Groups Waring Problem Group Theory
2011/9/13
Abstract: The classical Waring problem deals with expressing every natural number as a sum of g(k) kth powers. Similar problems for finite simple groups have been studied recently, and in this paper w...
Hyperbolicity of the complex of free factors
Hyperbolicity of the complex free factors Group Theory
2011/9/13
Abstract: We prove that the complex of free factors of a free group of finite rank is hyperbolic.
Bicyclic semigroups of left I-quotients
bicyclic semigroup bisimple inverse w-semigroup I-quotients Iorder
2011/9/13
Abstract: In this article we study left I-orders in the bicyclic monoid $\mathcal{B}$. We give necessary and sufficient conditions for a subsemigroup of $\mathcal{B}$ to be a left I-oreder in $\mathca...
Arbitrarily large families of spaces of the same volume
Arbitrarily large families Group Theory Geometric Topology
2011/9/9
Abstract: In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show th...
Linear estimates for solutions of quadratic equations in free groups
Linear estimates solutions of quadratic equations Group Theory
2011/9/6
Abstract: We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by $2s$ for orientable equation and by $12s^4$ for no...
Subdirect products of groups and the n-(n+1)-(n+2) theorem
fibre products subdirect products subgroup structure finiteness properties
2011/9/5
Abstract: We analyse the subgroup structure of direct products of groups. In particular, we seek to relate the finiteness properties of a group to the ways in which it embeds non-trivially into a dire...