  We consider the problem of embedding odometers in one-dimensional cellular
automata. We show that (1) every odometer can be be embedded in a gliders with
reflecting walls cellular automaton, which one depending on the odometer, and
(2) an odometer can be embedded in a cellular automaton, which is a group
endomorphism on an n-letter group, and where n depends on the odometer, if and
only if the odometer is "finitary."
