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Preprint Number 1228
1228. Udayan B. Darji, Márton Elekes, Kende Kalina, Viktor Kiss, Zoltán
Vidnyánszky The structure of random automorphisms E-mail: Submission date: 22 May 2017 Abstract: In order to understand the structure of the "typical" element of an
automorphism group, one has to study how large the conjugacy classes of the
group are. When typical is meant in the sense of Baire category, a complete
description of the size of the conjugacy classes has been given by Kechris and
Rosendal. Following Dougherty and Mycielski we investigate the measure
theoretic dual of this problem, using Christensen's notion of Haar null sets.
When typical means random, that is, almost every with respect to this notion of
Haar null sets, the behaviour of the automorphisms is entirely different from
the Baire category case. Mathematics Subject Classification: Primary 03E15, 22F50, Secondary 03C15, 28A05, 54H11, 28A99 Keywords and phrases: |

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