Minimal Number of Generators and Minimum Order of a Non-Abelian Group whose Elements Commute with Their Endomorphic Images
| dc.creator | Abdollahi, Alireza | |
| dc.creator | Faghihi, A. | |
| dc.creator | Hassanabadi, A. Mohammadi | |
| dc.date | 2007-08-16 | |
| dc.date.accessioned | 2026-07-07T08:24:02Z | |
| dc.date.available | 2026-07-07T08:24:02Z | |
| dc.description | A group in which every element commutes with its endomorphic images is called an $E$-group. If $p$ is a prime number, a $p$-group $G$ which is an $E$-group is called a $pE$-group. Every abelian group is obviously an $E$-group. We prove that every 2-generator $E$-group is abelian and that all 3-generator $E$-groups are nilpotent of class at most 2. It is also proved that every infinite 3-generator $E$-group is abelian. We conjecture that every finite 3-generator $E$-group should be abelian. Moreover we show that the minimum order of a non-abelian $pE$-group is $p^8$ for any odd prime number $p$ and this order is $2^7$ for $p=2$. Some of these results are proved for a class wider than the class of $E$-groups. | |
| dc.identifier | https://arxiv.org/abs/0708.2280 | |
| dc.identifier | http://arxiv.org/abs/0708.2280 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136208 | |
| dc.subject | Group Theory | |
| dc.subject | 20D45; 20E36 | |
| dc.title | Minimal Number of Generators and Minimum Order of a Non-Abelian Group whose Elements Commute with Their Endomorphic Images | |
| dc.type | text |