- International Electronic Journal of Algebra
- Vol: 16 Issue: 16
- ON NORMAL SUBGROUPS OF D∗ WHOSE ELEMENTS ARE PERIODIC MODULO THE CENTER OF D∗ OF BOUNDED ORDER
ON NORMAL SUBGROUPS OF D∗ WHOSE ELEMENTS ARE PERIODIC MODULO THE CENTER OF D∗ OF BOUNDED ORDER
Authors : Mai Hoang Bien
Pages : 66-71
Doi:10.24330/ieja.266227
View : 7 | Download : 4
Publication Date : 2014-12-01
Article Type : Other
Abstract :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 xnx ∈ 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.Keywords : Division ring, normal subgroup, radical, central