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Displaying 261 – 280 of 329

Existentially closed $L 𝔛$ -groups

Felix Leinen (1986)

Rendiconti del Seminario Matematico della Università di Padova

Existentially Closed Locally Finite Central Extensions: Multipliers and Local Systems.

Richard E. Phillips (1984)

Mathematische Zeitschrift

Expansion and random walks in ${SL}_{d} (ℤ / p^{n} ℤ)$ : I

Jean Bourgain, Alex Gamburd (2008)

Journal of the European Mathematical Society

We prove that the Cayley graphs of ${SL}_{d} (ℤ / p^{n} ℤ)$ are expanders with respect to the projection of any fixed elements in ${SL}_{d} (ℤ)$ generating a Zariski dense subgroup.

Expansion and random walks in ${SL}_{d} (ℤ / p^{n} ℤ)$ : II

Jean Bourgain, Alex Gamburd (2009)

Journal of the European Mathematical Society

Expansion in finite simple groups of Lie type

Emmanuel Breuillard, Ben J. Green, Robert Guralnick, Terence Tao (2015)

Journal of the European Mathematical Society

We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper [BGGT].

Expansion in $S L_{d} (𝒪_{K} / I)$ , $I$ square-free

Péter P. Varjú (2012)

Journal of the European Mathematical Society

Let $S$ be a fixed symmetric finite subset of $S L_{d} (𝒪_{K})$ that generates a Zariski dense subgroup of $S L_{d} (𝒪_{K})$ when we consider it as an algebraic group over $m a t h b b Q$ by restriction of scalars. We prove that the Cayley graphs of $S L_{d} (𝒪_{K} / I)$ with respect to the projections of $S$ is an expander family if $I$ ranges over square-free ideals of $𝒪_{K}$ if $d = 2$ and $K$ is an arbitrary numberfield, or if $d = 3$ and $K = ℚ$ .