Dihedral Groups as Epimorphic Images of Some Fibonacci Groups

Dihedral Groups as Epimorphic Images of Some Fibonacci Groups

The Fibonacci groups are defined by the presentation where ,  and all subscripts are assumed to be reduced modulo . In this paper we give an alternative proof that for , ,  and  are all infinite by establishing a morphism (or group homomorphism) onto the dihedral group  for all .

Bibliographic Details
Main Authors: Abdullahi Umar, Bashir Ali
Format: Article
Language:English
Published: Sultan Qaboos University 2013-12-01
Series:Sultan Qaboos University Journal for Science
Subjects:
Group
Fibonacci group
Dihedral group
(homo) Morphism.
Online Access:https://journals.squ.edu.om/index.php/squjs/article/view/416
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spelling doaj-aaa3307e77a24050965617903e745b7a2020-11-24T22:28:21ZengSultan Qaboos UniversitySultan Qaboos University Journal for Science1027-524X2414-536X2013-12-01180545910.24200/squjs.vol18iss0pp54-59411Dihedral Groups as Epimorphic Images of Some Fibonacci GroupsAbdullahi Umar0Bashir Ali1Department of Mathematics and Statistics, Sultan Qaboos University,Al-Khod, PC 123 – OmanDepartment of Mathematics and Computer Science, Nigerian Defence Academy, Kaduna – NigeriaThe Fibonacci groups are defined by the presentation where ,  and all subscripts are assumed to be reduced modulo . In this paper we give an alternative proof that for , ,  and  are all infinite by establishing a morphism (or group homomorphism) onto the dihedral group  for all .https://journals.squ.edu.om/index.php/squjs/article/view/416GroupFibonacci groupDihedral group(homo) Morphism.
collection DOAJ
language English
format Article
sources DOAJ
author Abdullahi Umar
Bashir Ali
spellingShingle Abdullahi Umar
Bashir Ali
Dihedral Groups as Epimorphic Images of Some Fibonacci Groups
Sultan Qaboos University Journal for Science
Group
Fibonacci group
Dihedral group
(homo) Morphism.
author_facet Abdullahi Umar
Bashir Ali
author_sort Abdullahi Umar
title Dihedral Groups as Epimorphic Images of Some Fibonacci Groups
title_short Dihedral Groups as Epimorphic Images of Some Fibonacci Groups
title_full Dihedral Groups as Epimorphic Images of Some Fibonacci Groups
title_fullStr Dihedral Groups as Epimorphic Images of Some Fibonacci Groups
title_full_unstemmed Dihedral Groups as Epimorphic Images of Some Fibonacci Groups
title_sort dihedral groups as epimorphic images of some fibonacci groups
publisher Sultan Qaboos University
series Sultan Qaboos University Journal for Science
issn 1027-524X
2414-536X
publishDate 2013-12-01
description The Fibonacci groups are defined by the presentation where ,  and all subscripts are assumed to be reduced modulo . In this paper we give an alternative proof that for , ,  and  are all infinite by establishing a morphism (or group homomorphism) onto the dihedral group  for all .
topic Group
Fibonacci group
Dihedral group
(homo) Morphism.
url https://journals.squ.edu.om/index.php/squjs/article/view/416
work_keys_str_mv AT abdullahiumar dihedralgroupsasepimorphicimagesofsomefibonaccigroups
AT bashirali dihedralgroupsasepimorphicimagesofsomefibonaccigroups
_version_ 1725746549566210048

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