I imagine a matrix group, with multiplication as the composition rule, to always possess the quality of having centre (I,-I), as I can't see when both elements wouldn't commute with all others. On the other hand, though, a centerless group is defined as having trivial centre, i.e. Z=I (which means, Z doesn't include -I). I imagine non-matrix groups could show this property, but I can't think of any. Could somebody give a couple of examples of centreless groups, and what "constraints" must be relaxed (from my matrix group example above) in order to achieve them?