Epimorphisms of compact groups are onto

Author:

Poguntke Detlev

Abstract

It is proved that the epimorphisms in the category of compact groups are surjective. The proof is based on the representation theory of compact groups, especially on the well-known fact, that for a closed proper subgroup H H of a compact group G G there exists an irreducible representation of G G which, when restricted to H H , contains the unit representation.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference2 articles.

1. L. Auslander, Unitary representations of locally compact groups, Lecture Note, Yale University, New Haven, Conn., 1961/62.

2. C. Chevalley, Theory of Lie groups, Princeton Math. Series, vol. 8, Princeton Univ. Press, Princeton, N. J., 1946. MR 7, 412.

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