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EnglishAccording 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.
| Titolo: | Finite morphic p-groups |
| Autori Unitn: | |
| Anno di pubblicazione: | 2015 |
| Titolo del periodico: | |
| Citazione: | 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. |
| 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. |
| Handle: | http://hdl.handle.net/11572/107391 |
| Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| 1411.0985v2.pdf | Articolo | Post-Print | Tutti i diritti riservati (All rights reserved) | Open Access Visualizza/Apri |
http://hdl.handle.net/11572/107391
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