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 : 13 | Download : 7

Publication Date : 2014-12-01

Article Type : Research Paper

Abstract :Let D be a division ring with the center F = Zinsert ignore into journalissuearticles values(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