ON NORMAL SUBGROUPS OF D∗ WHOSE ELEMENTS ARE PERIODIC MODULO THE CENTER OF D∗ OF BOUNDED ORDER

Mai Hoang Bien
2014 International Electronic Journal of Algebra  
Let D be a division ring with the center F = Z(D). Suppose that N is a normal subgroup of D * which is radical over F , that is, for any element x ∈ N , there exists a positive integer nx, such that x nx ∈ F . In [5], Herstein conjectured that N is contained in F . In this paper, we show that the conjecture is true if there exists a positive integer d such that nx ≤ d for any x ∈ N . Mathematics Subject Classification 2010: 16K20
doi:10.24330/ieja.266227 fatcat:pbepn5a2kfct7osqadejhyp6va