Abstract
In this paperG denotes a central topologicalT 2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is compact ([6], [5]). The purpose of this paper is to show, that if the componentG 0 of the identity is open,G′ must be compact, and to give an example of a compact group with (G/G 0)′ compact, whileG′ is not compact.
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