4.4 Centers

How do you compute the center of a group in Sage?

Although Sage calls GAP to do the computation of the group center, center is ``wrapped'' (i.e., Sage has a class PermutationGroup with associated class method ``center''), so the user does not need to use the gap command. Here's an example:

sage: G = PermutationGroup(['(1,2,3)(4,5)', '(3,4)'])
sage: G.center()
Permutation Group with generators [()]

A similar syntax for matrix groups also works:

sage: G = SL(2, GF(5) )
sage: G.center()
Matrix group over Finite Field of size 5 with 1 generators:
 [[[4, 0], [0, 4]]] 
sage: G = PSL(2, 5 )
sage: G.center()
Permutation Group with generators [()]

Note: center can be spelled either way in GAP, not so in Sage.

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