**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)**

## Details

### 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).

## Related papers

- Shannon, A. G., Erdağ, O., & Deveci, Ö. (2021). On the connections between Pell numbers and Fibonacci
*p*-numbers.*Notes on Number Theory and Discrete Mathematics*, 21(1), 148–160.

## Cite this paper

Mehraban, E., Deveci, Ö., & Hincal, E. (2024). The generalized order (*k*,*t*)-Mersenne sequences in groups. *Notes on Number Theory and Discrete Mathematics*, 30(2), 271-282, DOI: 10.7546/nntdm.2024.30.2.271-282.