On Some Results of a Torsion-Free Abelian Trace Group

Abstract

In [6], givenany torsion-free abelian groups Gand H, the pure trace of Hin Gis *,:,GHHomfHfGHtr which is equivalent to the set ZnGHHomfHfngGgsomefor ,,:.The pure trace GHtr, is a pure fully invariant subgroup of G. A torsion-free abelian group Gis a trace group if for every pure fully invariant subgroup Mof G, .,GMtrMIn this paper, we giv further results of pure trace, trace group and characterize the direct sum of the trace groups of a torsion-free abelian groups.

Keywords

• trace group
• pure trace
• torsion-free abelian group
• direct sum
• pure fully invariant