On normal subgroups of \(D^*\) whose elements are periodic modulo the center of \(D^*\) of bounded order. (Q2879411)

Let \(D\) be a division ring with center \(F\) and \(N\) a normal subgroup of the multiplicative group \(D^*\) of \(D\). In the article under review, the author proves that if there exists a positive integer \(d\) such that \(x^d\in F\) for any \(x\in N\), then \(N\) is contained in \(F\), which answers partially a conjecture proposed by \textit{I. N. Herstein} [Isr. J. Math. 31, 180-188 (1978; Zbl 0394.16015)]. The idea of the proof is to show that \(N\) satisfies a nontrivial generalized rational identity over \(D\).