Finite simple groups of Lie type as expanders

Alexander Lubotzky

Displaying similar documents to “Finite simple groups of Lie type as expanders”

Covering locally compact groups by less than $2^{ω}$ many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

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Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if $C_{E K}$ is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of $C_{E K}$ . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result...

Lie groups and $p$ -compact groups.

Dwyer, W.G. (1998)

Documenta Mathematica

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Compact Abelian groups and extensions of Haar measures

A. Hulanicki

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ContentsIntroduction.................................................................................................................... 31. Preliminaries (topology measure).................................................................... 32. Problems and the theorem.................................................................................... 73. Preliminaries (abstract groups, Cartesian products)....................................... 94. Preliminaries (automorphisms, duality...

$1 \frac{1}{2}$ -generation of finite simple groups.

Stein, Alexander (1998)

Beiträge zur Algebra und Geometrie

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On groups with root system of type $^{2} F_{4}$ .

Oueslati, H. (2009)

Beiträge zur Algebra und Geometrie

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Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi (2014)

Annales de l’institut Fourier

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In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type $☆$ ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type $☆$ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...

On countable extensions of primary abelian groups

Peter Vassilev Danchev (2007)

Archivum Mathematicum

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It is proved that if $A$ is an abelian $p$ -group with a pure subgroup $G$ so that $A / G$ is at most countable and $G$ is either $p^{ω + n}$ -totally projective or $p^{ω + n}$ -summable, then $A$ is either $p^{ω + n}$ -totally projective or $p^{ω + n}$ -summable as well. Moreover, if in addition $G$ is nice in $A$ , then $G$ being either strongly $p^{ω + n}$ -totally projective or strongly $p^{ω + n}$ -summable implies that so is $A$ . This generalizes a classical result of Wallace (J. Algebra, 1971) for totally projective $p$ -groups as well as continues our recent investigations...

The measurability of Lie groups

G. Vranceanu (1964)

Annales Polonici Mathematici

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Growth in ${SL}_{3} (ℤ / p ℤ)$

H. A. Helfgott (2011)

Journal of the European Mathematical Society

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Simply connected coset complexes for rank 1 groups of Lie type.

Yoav Segev (1994)

Mathematische Zeitschrift

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Notes on countable extensions of $p^{ω + n}$ -projectives

Peter Vassilev Danchev (2008)

Archivum Mathematicum

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We prove that if $G$ is an Abelian $p$ -group of length not exceeding $ω$ and $H$ is its $p^{ω + n}$ -projective subgroup for $n \in ℕ \cup {0}$ such that $G / H$ is countable, then $G$ is also $p^{ω + n}$ -projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971).