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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The projective dimension of a compact abelian group


Author: Eric C. Nummela
Journal: Proc. Amer. Math. Soc. 38 (1973), 452-456
MSC: Primary 18G05; Secondary 22B05
MathSciNet review: 0313362
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Abstract: Let $ X$ be a compact group, $ FGX$ the (Graev) free topological group generated by $ X$, and $ K$ the kernel of the canonical quotient morphism from $ FGX$ to $ X$. Then $ K$ is a (Graev) free topological group. A corollary to the abelian analogue of this theorem is that the projective dimension of a compact abelian group, relative to the class of all continuous epimorphisms admitting sections, is exactly one.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0313362-4
PII: S 0002-9939(1973)0313362-4
Keywords: Markov free topological group, Graev free topological group, projective abelian group, Schreier system
Article copyright: © Copyright 1973 American Mathematical Society