Some Constructions of a strongly co-hopfian Abelian Groups

Seddik Abdelalim; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 94

Some Constructions of a strongly co-hopfian Abelian Groups

Seddik Abdelalim

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Jan 23, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: An abelian group $A$ is called strongly co-hopfian if for every endomorphism $\alpha$ of $A$ the chain $Im(\alpha )\supseteq Im(\alpha^{2})\supseteq Im(\alpha^{3})\supseteq Im(\alpha^{4})\supseteq \cdots $ is stationary. In this work we characterize some properties of the strongly co-hopfian abelian group. Then we show that the p-component of strongly co-hopfian abelian group is also strongly co-hopfian but for the torsion part we construct strongly co-hopfian abelian group whose the torsion part is not strongly co-hopfian.