Finite morphic $p$groups
Abstract
According to Li, Nicholson and Zan, a group $G$ is said to be morphic if, for every pair $N_{1}, N_{2}$ of normal subgroups, each of the conditions $G/N_{1} \cong N_{2}$ and $G/N_{2} \cong N_{1}$ implies the other. Finite, homocyclic $p$groups are morphic, and so is the nonabelian group of order $p^{3}$ and exponent $p$, for $p$ an odd prime. It follows from results of An, Ding and Zhan on self dual groups that these are the only examples of finite, morphic $p$groups. In this paper we obtain the same result under a weaker hypotesis.
 Publication:

arXiv eprints
 Pub Date:
 November 2014
 DOI:
 10.48550/arXiv.1411.0985
 arXiv:
 arXiv:1411.0985
 Bibcode:
 2014arXiv1411.0985C
 Keywords:

 Mathematics  Group Theory;
 20D15
 EPrint:
 7 pages. Critical reference added, and manuscript revised accordingly