We suggest a method of a computation of hyperfine anomaly for many-electron atoms and ions. At first, we tested this method by calculating the hyperfine anomaly for a hydrogen-like thallium ion and obtained fairly good agreement with analytical expressions. Then, we did calculations for the neutral thallium and tested an assumption that the ratio between the anomalies for s and p1/2 states is the same for these two systems. Finally, we come up with recommendations about the preferable atomic states for the precise measurements of the nuclear g factors.

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