|
| << vorige | volgende >> |
Tijdschrift beschrijving
Alle jaargangen van het bijbehorende tijdschrift
Alle afleveringen van het bijbehorende jaargang
Alle artikelen van de bijbehorende aflevering
Details van artikel 10 van 28 gevonden artikelen
| Titel: |
Minimal Number of Generators and Minimum Order of a Non-Abelian Group Whose Elements Commute with Their Endomorphic Images |
| Auteur: |
Abdollahi, A. Faghihi, A. Hassanabadi, A. Mohammadi |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 36 (2008) nr. 5 pagina's 1976-1987 |
| Jaar: |
2008-05 |
| Inhoud: |
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 p8 for any odd prime number p and this order is 27 for p = 2. Some of these results are proved for a class wider than the class of E-groups. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 10 van 28 gevonden artikelen
| << vorige | volgende >> |