Integer group determinants for \(\mathrm{C}_4^2 \) (Q6542797)

Let \(G=\{g_1,\dots,g_n\}\) be a group. Assign to each \(g\in G\) an integer variable \(x_g\). The integer group determinant of \(G\) is the determinant of the \(n\times n\) matrix with \((i,j)\)th entry \(x_{g_ig_j^{-1}}\). Let \(S(G)\) be the set of all its possible values.\N\NLet \(C_4\) be the cyclic group of order 4. The authors determine \(S(C_4^2)\). They have previously [Ramanujan J. 62, 983--995 (2023; Zbl 1548.11062)] determined \(S(C_2^4)\). Also several related sets have been found by them and other authors.