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).(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Centerless groups

**Physics Forums | Science Articles, Homework Help, Discussion**