%0 Journal Article
%T The Quasi-morphic Property of Group
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Wang, Q.
%A Long, K.
%A Feng, L.
%D 2013
%\ 03/01/2013
%V 39
%N 1
%P 175-185
%! The Quasi-morphic Property of Group
%K quasi-morphic group
%K finitely generated abelian group
%K normal endomorphism
%R
%X A group is called morphic if for each normal endomorphism α in end(G),there exists β such that ker(α)= Gβ and Gα= ker(β). In this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= Gβ and Gα = ker(γ). We call G quasi-morphic, if this happens for any normal endomorphism α in end(G). We get the following results: G is quasi-morphic if and only if, for any normal subgroup K and N such that G/K≌N, there exist normal subgroup T and H such that G/T≌K and G/N≌H. Further, we investigate the quasi-morphic property of finitely generated abelian group and get that a finitely generated abelian group is quasi-morphic if and only if it is finite.
%U http://bims.iranjournals.ir/article_339_e1fa74b090c7cf943c21d3c24a31908a.pdf