Results 1 to 10 of about 13,551 (107)
Normal Subgroup Growth of Linear Groups: the (G2; F4;E8)-Theorem [PDF]
, 2011 Let G be a finitely generated group and M_n(G) the number of its normal subgroup subgroups of index at most n. For linear groups G we show that M_n(G) can grow polynomially in n only if the semisimple part of the Zariski closure of G has simple components only of type G2, F4 or E8 (and in this case indeed this can happened!)
Larsen, Michael, Lubotzky, Alexander
openaire +3 more sources
Small doubling in groups [PDF]
, 2013 Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A|
A. G. Vosper +61 more
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Representation growth and representation zeta functions of groups [PDF]
, 2012 We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic groups, such as ...
Klopsch, Benjamin
core +3 more sources
On groups and counter automata [PDF]
, 2006 We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this ...
Dixon J. D. +8 more
core +2 more sources
On Fields of rationality for automorphic representations [PDF]
, 2014 This paper proves two results on the field of rationality $\Q(\pi)$ for an automorphic representation $\pi$, which is the subfield of $\C$ fixed under the subgroup of $\Aut(\C)$ stabilizing the isomorphism class of the finite part of $\pi$.
Nicolas Templier, Shin, Sug Woo
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3-manifold groups are virtually residually p [PDF]
, 2012 Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite index subgroup which is residually $p$.
Matthias Aschenbrenner +2 more
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Properties of centered random walks on locally compact groups and Lie groups
, 2007 The basic aim of this paper is to study asymptotic properties of the convolution powers K^(n) = K * K * ... * K of a possibly non-symmetric probability density K on a locally compact, compactly generated group G. If K is centered, we show that the Markov
Dungey, Nick
core +2 more sources
Shintani functions, real spherical manifolds, and symmetry breaking operators
, 2014 For a pair of reductive groups $G \supset G'$, we prove a geometric criterion for the space $Sh(\lambda, \nu)$ of Shintani functions to be finite-dimensional in the Archimedean case. This criterion leads us to a complete classification of the symmetric
B. Kostant +6 more
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Growth of quasiconvex subgroups
, 2018 We prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron-Frobenius theory.
Dahmani, François +2 more
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, 2010 This is an informal announcement of results to be described and proved in detail in a paper to appear. We give various results on the structure of approximate subgroups in linear groups such as $\SL_n(k)$.
Breuillard, Emmanuel +2 more
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