- #1

Spriteling

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## Homework Statement

Show that the group G where [itex]G = \left(\begin{array}{ccc} \cos\theta & -

sin\theta & u \\ \sin\theta & \cos\theta & v \\ 0 & 0 & 1 \end{array} \right) u,v \in \Re, \theta \in \Re/2\pi Z [/itex]

## Homework Equations

I know that a set is connected if it is not the disjoint union of two non-empty sets, if any two elements in G can be joined by a [itex]C^k[/itex] path in G, and if G is generated by a neighbourhood of 1.

## The Attempt at a Solution

I thought that it would be easiest to show that G is not the disjoint union of two non-empty sets, and I was trying to do it by contradiction, but got nowhere.

Any hints/nudges in the right direction would be appreciated.