TY - JOUR
ID - 339
TI - The Quasi-morphic Property of Group
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Wang, Q.
AU - Long, K.
AU - Feng, L.
AD - Department of Mathematics and Systems Science, National University of Defense Technology, P.R.China 410073,Changsha, China.
AD - Department of Mathematics and Systems Science, National University of Defense Technology ,P.R.China 410073, Changsha, China.
AD - Department of Mathematics and Systems Science, National University of Defense
Technology, P.R.China 410073, Changsha, China.
Y1 - 2013
PY - 2013
VL - 39
IS - 1
SP - 175
EP - 185
KW - quasi-morphic group
KW - finitely generated abelian group
KW - normal endomorphism
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_339.html
L1 - http://bims.iranjournals.ir/article_339_e1fa74b090c7cf943c21d3c24a31908a.pdf
ER -