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I was doing a homework question about computing the center of a group, and realized everytime I've ever computed the center, I am very explicitly writing down elements and finding restrictions.

I would like to expand my reservoir of tricks; are there any examples of specific (or a class of) groups with a nice trick to compute the center?

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    $\begingroup$ Is there a reason to expect an easier way that works generally? $\endgroup$ Commented 14 hours ago
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    $\begingroup$ It seems a vague request - there are lots of ways to define a group. $\endgroup$ Commented 14 hours ago
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    $\begingroup$ For instance, for groups given by a finite presentation, the problem of determining if they have trivial center is (algorithmically) undecidable. $\endgroup$ Commented 13 hours ago
  • $\begingroup$ @ThomasAndrews I am not asking for in general, but just nice tricks for particular groups that might help in future calculations $\endgroup$ Commented 10 hours ago
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    $\begingroup$ And yet, you haven't given a single example of what kind of problems you've seen. Without being more specific, nobody can be any help. $\endgroup$ Commented 9 hours ago

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