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could any one give me hint for this one?

$G$ be a connected group, and let $H$ be a discrete normal subgroup of $G$, then we need to show $H$ is contained in the center of $G$

first of all, I have no clear idea what is meant by discrete subgroup and its any special properties?

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A discrete subgroup is just a subgroup such that the subspace topology it gets as a subset of $G$ is the same as the discrete topology. – Zev Chonoles Jan 26 '13 at 6:59
an example will be appreciated – Un Chien Andalou Jan 26 '13 at 7:00
An example: circle group and $n$-th root of unity. – user27126 Jan 26 '13 at 7:07
Hint: Fix $h \in H$. What must the set $ghg^{-1}$ be, using connectedness? – user27126 Jan 26 '13 at 7:08
up vote 6 down vote accepted

Hint, See: Lecture V - Topological Groups, Theorem 5.5.

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