Results 1 to 10 of about 13,678 (125)

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

Probabilistic nilpotence in infinite groups [PDF]

, 2020
The 'degree of k-step nilpotence' of a finite group G is the proportion of the tuples (x_1,...,x_{k+1}) in G^{k+1} for which the simple commutator [x_1,...,x_{k+1}] is equal to the identity. In this paper we study versions of this for an infinite group G,
Martino, Armando, Tointon, Matthew, Valiunas, Motiejus, Ventura, Enric   +3 more
core   +2 more sources

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 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
core   +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, A. L. Cauchy, A. Lubotzky, A. Lubotzky, A. S. Golsefidy, B. Green, B. Green, B. Green, B. Green, B. Green, C. Even-Zohar, D. Fisher, E. Breuillard, E. Breuillard, E. Breuillard, E. Croot, E. Hrushovski, G. A. Freiman, G. A. Freiman, G. A. Margulis, G. Elekes, G. Petridis, H. A. Helfgott, H. A. Helfgott, H. Davenport, I. Z. Ruzsa, I. Z. Ruzsa, I. Z. Ruzsa, J. Bourgain, J. Bourgain, J. D. Dixon, L. Dries van den, M. Gromov, M. J. Larsen, M. Kassabov, M. Kneser, M.-C. Chang, M.-C. Chang, P. P. Varjú, P. Sarnak, P. Sarnak, R. I. Grigorchuk, R. J. Gardner, S. Hoory, S. R. Safin, S. V. Konyagin, T. Coulhon, T. Sanders, T. Sanders, T. Sanders, T. Sanders, T. Schoen, T. Tao, T. Tao, T. Tao, V. F. Lev, W. T. Gowers, W. T. Gowers, W. Woess, Y. Shalom, Y. Stanchescu, Y. Stanchescu   +61 more
core   +1 more source

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, Sr. M. Benigna Fehlner, Stefan Friedl   +2 more
core   +1 more source

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

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, Futer, David, Wise, Daniel T.   +2 more
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, B. Sun, M. Berger, M. Kashiwara, S. Helgason, S. Helgason, T. Oshima   +6 more
core   +1 more source

Profinite completion of Grigorchuk's group is not finitely presented

, 2012
In this paper we prove that the profinite completion $\mathcal{\hat G}$ of the Grigorchuk group $\mathcal{G}$ is not finitely presented as a profinite group.
de la Harpe P., Grigorchuk R. I., Grigorchuk R. I., Karpilovsky G., Lysënok I. G., MUSTAFA GÖKHAN BENLI, Wilson J. S.   +6 more
core   +1 more source