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Is the following statement true or not?

A locally compact Hausdorff space $X$ is a group if and only if its Stone–Čech compactification$\beta X$ is a group.

Thanks.

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    $\beta\mathbb{Z}$ is not a group, I believe, while $\mathbb{Z}$ is...2012-12-22
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    In general (see http://dutiaw37.twi.tudelft.nl/~kp/onderwijs/topologie/d17-betaX.pdf, e.g.) we have that a pseudocompact (Tychonoff) topological group is such that its group operations can be extended to its Cech-Stone compactification.2012-12-22
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    You should explain what "is a group" means.2012-12-22
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    There is a way to compactify topological groups (http://en.wikipedia.org/wiki/Bohr_compactification) but the underlying topological space of the Bohr compactification isn't the Stone-Cech compactification. For example, the Bohr compactification of $\mathbb{Z}$ is the Pontrjagin dual of $S^1$ with the discrete topology...2012-12-22
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    Here a group means that it is a topological group under the given topology.2012-12-23

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