On Square Roots of the Uniform Distribution on Compact Groups
- 1 October 1986
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 98 (2) , 341-348
- https://doi.org/10.2307/2045709
Abstract
Let be a compact separable topological group. When does there exist a probability such that , where is Haar measure and ? We show that such square roots exist if and only if is not abelian, nor the product of the quaternions and a product of two element groups. In the course of proving this we classify compact groups with the property that every closed subgroup is normal.Keywords
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