The generalized order (k,t)-Mersenne sequences in groups

E. Mehraban, Ö. Deveci, E. Hincal
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 2, Pages 271–282
DOI: 10.7546/nntdm.2024.30.2.271-282
Full paper (PDF, 302 Kb)

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Authors and affiliations

E. Mehraban
¹ Mathematics Research Center, Near East University TRNC, Mersin 10, 99138 Nicosia, Turkey
² Department of Mathematics, Near East University TRNC, Mersin 10, 99138 Nicosia, Turkey
³ Faculty of Art and Science, University of Kyrenia TRNC, Mersin 10, 99320 Kyrenia, Turkey

Ö. Deveci
Department of Mathematics, Faculty of Science and Letters, Kafkas University
36100, Turkey

E. Hincal
¹ Mathematics Research Center, Near East University TRNC, Mersin 10, 99138 Nicosia, Turkey
² Department of Mathematics, Near East University TRNC, Mersin 10, 99138 Nicosia, Turkey
³ Faculty of Art and Science, University of Kyrenia TRNC, Mersin 10, 99320 Kyrenia, Turkey

Abstract

The purpose of this paper is to determine the algebraic properties of finite groups via a Mersenne-like sequence. Firstly, we introduce the generalized order -Mersenne number sequences and study the periods of these sequences modulo . Then, we get some interesting structural results. Furthermore, we expand the generalized order -Mersenne number sequences to groups and we give the definition of the generalized order -Mersenne sequences, , in the -generator groups and also, investigate these sequences in the non-Abelian finite groups in detail. At last, we obtain the periods of the generalized order -Mersenne sequences in some special groups as applications of the results produced.

Keywords

• Period
• Mersenne number
• The generalized order -Mersenne number sequences -group

2020 Mathematics Subject Classification

• 20F05
• 11B39
• 20D60

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Manuscript history

• Received: 22 February 2023
• Revised: 11 May 2024
• Accepted: 15 May 2024
• Online First: 17 May 2024

Copyright information

Ⓒ 2024 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).