Resumen de Morphic p-groups

Farid Aliniaeifard, Yuanlin Li, W. K. Nicholson

• A group G is called morphic if every endomorphism ¦Á : G ¡ú G for which G¦Á is normal in G satisfies G/G¦Á ¡«= ker(¦Á). This concept for modules was first investigated by G. Ehrlich in 1976. Since then the concept has been extensively studied in module and ring theory.

  A recent paper of Li, Nicholson and Zan investigated the idea in the category of groups.

  A characterization for a finite nilpotent group to be morphic was obtained, and some results about when a small p-group is morphic were given. In this paper, we continue the investigation of the general finite morphic p-groups. Necessary and sufficient conditions for a morphic p-group of order pn(n > 3) to be abelian are given. Our main results show that if G is a morphic p-group of order pn with n > 3 such that either d(G) = 2 or | G¡ä |< p3, then G is abelian, where d(G) is the minimal number of generators of G. As consequences of our main results we show that any morphic p-groups of order p4, p5 and p6 are abelian.