**Bishnu Paudel and Chris Pinner**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 29, 2023, Number 3, Pages 603–619

DOI: 10.7546/nntdm.2023.29.3.603-619

**Full paper (PDF, 293 Kb)**

## Details

### Authors and affiliations

Bishnu Paudel

*Department of Mathematics, Kansas State University
Manhattan KS 66506, United States*

Chris Pinner

*Department of Mathematics, Kansas State University
Manhattan KS 66506, United States*

### Abstract

Let denote the cyclic group of order . We show how the group determinant for can be simply written in terms of the group determinant for . We use this to get a complete description of the integer group determinants for where is the dihedral group of order , and where is the quaternion group of order .

### Keywords

- Integer group determinant
- Dihedral group
- Quaternion group

### 2020 Mathematics Subject Classification

- 11C20
- 15B36
- 11C08
- 43A40

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### Manuscript history

- Received: 22 March 2023
- Revised: 4 August 2023
- Accepted: 11 August 2023
- Online First: 25 August 2023

### Copyright information

Ⓒ 2023 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).

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## Cite this paper

Paudel, B, & Pinner, C. (2023). The group determinants for ℤ_{n} × *H*. *Notes on Number Theory and Discrete Mathematics*, 29(3), 603-619, DOI: 10.7546/nntdm.2023.29.3.603-619.