## Groups with finite dimensional irreducible representations

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- by Calvin C. Moore PDF
- Trans. Amer. Math. Soc.
**166**(1972), 401-410 Request permission

## Abstract:

It will be shown that a locally compact group has a finite bound for the dimensions of its irreducible unitary representations if and only if it has a closed abelian subgroup of finite index. It will further be shown that a locally compact group has all of its irreducible representations of finite dimension if and only if it is a projective limit of Lie groups with the same property, and finally that a Lie group has this property if and only if it has a closed subgroup*H*of finite index such that

*H*modulo its center is compact.

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## Additional Information

- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**166**(1972), 401-410 - MSC: Primary 22D10
- DOI: https://doi.org/10.1090/S0002-9947-1972-0302817-8
- MathSciNet review: 0302817