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The integer group determinants do not determine the group

Humberto Bautista Serrano, Bishnu Paudel and Chris Pinner

Vol. 13 (2024), No. 1, 59–65
DOI: 10.2140/cnt.2024.13.59
Abstract

We obtain a complete description of the integer group determinants for SmallGroup (16,13), the central product of the dihedral group of order 8 and cyclic group of order 4.

These values are the same as the integer group determinants for SmallGroup (16,11), the direct product of the dihedral group of order 8 and cyclic group of order 2. It was not previously known that the integer group determinants do not determine the group.

Keywords
integer group determinants, small groups, dihedral group, quaternion group, central product
Mathematical Subject Classification
Primary: 11C20, 15B36
Secondary: 11C08, 43A40
Milestones
Received: 9 April 2023
Revised: 26 January 2024
Accepted: 13 February 2024
Published: 13 March 2024
Authors
Humberto Bautista Serrano
Department of Mathematics
Kansas State University
Manhattan, KS
United States
Bishnu Paudel
Department of Mathematics
Kansas State University
Manhattan, KS
United States
Chris Pinner
Department of Mathematics
Kansas State University
Manhattan, KS
United States