Almost independence and irreducibility in simple finite and algebraic groups

Aner Shalev

doi:10.1016/j.jalgebra.2017.03.014

Almost independence and irreducibility in simple finite and algebraic groups

Aner Shalev

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

We study intersections of the form g₁C₁∩g₂C₂, where C_i are conjugacy classes of arbitrary finite simple groups and g_i are group elements. We show that, generically, |g₁C₁∩g₂C₂|∼|C₁||C₂|/|G|, which means that the events g₁C₁,g₂C₂ are almost independent in G. We also discuss the dimension and the irreducibility of such intersections in simple algebraic groups, and expose the anomaly of SL₂. This work is motivated by recent questions of Hrushovski.

Original language	English
Pages (from-to)	375-389
Number of pages	15
Journal	Journal of Algebra
Volume	500
DOIs	https://doi.org/10.1016/j.jalgebra.2017.03.014
State	Published - 15 Apr 2018

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© 2017 Elsevier Inc.

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Zelmanov issue

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10.1016/j.jalgebra.2017.03.014

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abstract = "We study intersections of the form g1C1∩g2C2, where Ci are conjugacy classes of arbitrary finite simple groups and gi are group elements. We show that, generically, |g1C1∩g2C2|∼|C1||C2|/|G|, which means that the events g1C1,g2C2 are almost independent in G. We also discuss the dimension and the irreducibility of such intersections in simple algebraic groups, and expose the anomaly of SL2. This work is motivated by recent questions of Hrushovski.",

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ER -

Almost independence and irreducibility in simple finite and algebraic groups

Abstract

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