Geodesic
The topological center of the semigroup of free ultrafilters
Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 437-441

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For any group $G$, it is proved that the topological center of the semigroup of free ultrafilters on the group $G$ is empty. 
@article{MZM_1998_63_3_a14,
     author = {I. V. Protasov},
     title = {The topological center of the semigroup of free ultrafilters},
     journal = {Matemati\v{c}eskie zametki},
     pages = {437--441},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a14/}
}
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I. V. Protasov. The topological center of the semigroup of free ultrafilters. Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 437-441. http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a14/