Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Central idempotent measures on compact groups
HTML articles powered by AMS MathViewer

by Daniel Rider PDF
Trans. Amer. Math. Soc. 186 (1973), 459-479 Request permission


Let G be a compact group with dual object $\Gamma = \Gamma (G)$ and let $M(G)$ be the convolution algebra of regular finite Borel measures on G. The author has characterized the central idempotent measures on certain G, including the unitary groups, in terms of the hypercoset structure of $\Gamma$. The characterization also says that, on certain G, a central idempotent measure is a sum of such measures each of which is absolutely continuous with respect to the Haar measure of a closed normal subgroup. The main result of this paper is an extension of this characterization to products of certain groups. The known structure of connected groups and a recent result of Ragozin on connected simple Lie groups will then show that the characterization is valid for connected groups. On the other hand, a simple example will show it is false in general for non-connected groups. This characterization was done by Cohen for abelian groups and the proof borrows extensively from Amemiya and Itô’s simplified proof of Cohen’s result.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A05, 22C05
  • Retrieve articles in all journals with MSC: 43A05, 22C05
Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 186 (1973), 459-479
  • MSC: Primary 43A05; Secondary 22C05
  • DOI:
  • MathSciNet review: 0340961