The integer group determinants for SmallGroup(16,13)
Humberto Bautista Serrano, Bishnu Paudel, Chris Pinner
TL;DR
This paper fully characterizes the integer group determinants for a specific group, revealing that these determinants do not uniquely identify the group, contrasting with prior assumptions.
Contribution
It provides the first complete description of integer group determinants for SmallGroup(16,13), showing they coincide with those of another group and do not uniquely determine the group.
Findings
Integer group determinants for SmallGroup(16,13) are fully described.
These determinants match those of SmallGroup(16,11).
Integer group determinants do not uniquely identify the group.
Abstract
We obtain a complete description of the integer group determinants for SmallGroup(16,13), the central product of the dihedral group of order eight and cyclic group of order four. These values are the same as the integer group determinants for SmallGroup(16,11), the direct product of the dihedral group of order eight and cyclic group of order two. It was not previously known that the integer group determinants do not determine the group.
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Taxonomy
Topicsgraph theory and CDMA systems · Finite Group Theory Research · Advanced Combinatorial Mathematics