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.

Finite morphic p-groups / Caranti, Andrea; Scoppola, C. M.. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 2015:10(2015), pp. 4635-4641. [10.1016/j.jpaa.2015.02.035]

Finite morphic p-groups

Caranti, Andrea;
2015

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.
10
Caranti, Andrea; Scoppola, C. M.
Finite morphic p-groups / Caranti, Andrea; Scoppola, C. M.. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 2015:10(2015), pp. 4635-4641. [10.1016/j.jpaa.2015.02.035]
File in questo prodotto:
File Dimensione Formato  
1411.0985v2.pdf

accesso aperto

Descrizione: Articolo
Tipologia: Post-print referato (Refereed author’s manuscript)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 119.52 kB
Formato Adobe PDF
119.52 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/107391
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact