The quaternion-Pell sequence

Deveci, Ö; Shannon, AG

The quaternion-Pell sequence

Deveci, Ö Shannon, AG

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Publication Type:: Journal Article
Citation:: Communications in Algebra, 2018, 46 (12), pp. 5403 - 5409
Issue Date:: 2018-12-02

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Field	Value	Language
dc.contributor.author	Deveci, Ö	en_US
dc.contributor.author	Shannon, AG https://orcid.org/0000-0003-0116-0666	en_US
dc.date.issued	2018-12-02	en_US
dc.identifier.citation	Communications in Algebra, 2018, 46 (12), pp. 5403 - 5409	en_US
dc.identifier.issn	0092-7872	en_US
dc.identifier.uri	http://hdl.handle.net/10453/132117
dc.description.abstract	© 2018, © 2018 Taylor & Francis. In this paper, we define the quaternion-Pell sequence and derive the generating matrix of the sequence. Then we produce the semigroups using the multiplicative orders of the generating matrix of the quaternion-Pell sequence when read modulo α. We also study the quaternion-Pell sequence modulo α and then we give the relationship among the periods of the quaternion-Pell sequence modulo α and the orders of the semigroups obtained. In addition, we extend the quaternion-Pell sequence to groups. Finally, we obtain the periods of the quaternion-Pell sequences in dihedral groups D 2m as applications of the results obtained.	en_US
dc.relation.ispartof	Communications in Algebra	en_US
dc.relation.isbasedon	10.1080/00927872.2018.1468906	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	The quaternion-Pell sequence	en_US
dc.type	Journal Article
utslib.citation.volume	12	en_US
utslib.citation.volume	46	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access
pubs.issue	12	en_US
pubs.publication-status	Published	en_US
pubs.volume	46	en_US

Abstract:

© 2018, © 2018 Taylor & Francis. In this paper, we define the quaternion-Pell sequence and derive the generating matrix of the sequence. Then we produce the semigroups using the multiplicative orders of the generating matrix of the quaternion-Pell sequence when read modulo α. We also study the quaternion-Pell sequence modulo α and then we give the relationship among the periods of the quaternion-Pell sequence modulo α and the orders of the semigroups obtained. In addition, we extend the quaternion-Pell sequence to groups. Finally, we obtain the periods of the quaternion-Pell sequences in dihedral groups D 2m as applications of the results obtained.

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http://hdl.handle.net/10453/132117