The maximal abelian subextension determines weak mixing for group extensions

Author:
E. Arthur Robinson

Journal:
Proc. Amer. Math. Soc. **114** (1992), 443-450

MSC:
Primary 28D05; Secondary 22D40

DOI:
https://doi.org/10.1090/S0002-9939-1992-1062835-X

MathSciNet review:
1062835

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Abstract: Weak mixing is an important property for group extensions because its absence is the principal obstruction to lifting a large number of stronger mixing properties. Whether or not an extension is weakly mixing can be determined by studying the sub-extension corresponding to the quotient by the commutator subgroup. Several conditions equivalent to weak mixing are given. In particular, an extension by any group with no abelian factors (for example any nonabelian simple group) is automatically weak mixing if it is ergodic. The proof uses spectral multiplicity theory.

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DOI:
https://doi.org/10.1090/S0002-9939-1992-1062835-X

Article copyright:
© Copyright 1992
American Mathematical Society