Bien, Mai Hoang On normal subgroups of \(D^*\) whose elements are periodic modulo the center of \(D^*\) of bounded order. (English) Zbl 1325.16033 Int. Electron. J. Algebra 16, 66-71 (2014). 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 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 \(D\). Reviewer: Bui Xuan Hai (Ho Chi Minh City) Cited in 2 Documents MSC: 16U60 Units, groups of units (associative rings and algebras) 16K40 Infinite-dimensional and general division rings 16K20 Finite-dimensional division rings 16R50 Other kinds of identities (generalized polynomial, rational, involution) 20E15 Chains and lattices of subgroups, subnormal subgroups 20E07 Subgroup theorems; subgroup growth Keywords:division rings; normal subgroups of multiplicative groups; generalized rational identities; radical subgroups; central subgroups; unit groups Citations:Zbl 0394.16015 PDFBibTeX XMLCite \textit{M. H. Bien}, Int. Electron. J. Algebra 16, 66--71 (2014; Zbl 1325.16033) Full Text: DOI arXiv Link