Almost independence and irreducibility in simple finite and algebraic groups

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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.

Original languageAmerican English
Pages (from-to)375-389
Number of pages15
JournalJournal of Algebra
StatePublished - 15 Apr 2018

Bibliographical note

Funding Information:
The author acknowledges the support of an Israel Science Foundation grant 1117/13, and of the Vinik Chair of Mathematics which he holds.

Publisher Copyright:
© 2017 Elsevier Inc.


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