Rocky Mountain Journal of Mathematics

The integer group determinants for the symmetric group of degree four

Christopher Pinner

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For the symmetric group $S_4$ we determine all the integer values taken by its group determinant when the matrix entries are integers.

Article information

Rocky Mountain J. Math., Volume 49, Number 4 (2019), 1293-1305.

First available in Project Euclid: 29 August 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure 15B36: Matrices of integers [See also 11C20]
Secondary: 11B83: Special sequences and polynomials 11C08: Polynomials [See also 13F20] 11C20: Matrices, determinants [See also 15B36] 11G50: Heights [See also 14G40, 37P30] 11R09: Polynomials (irreducibility, etc.) 11T22: Cyclotomy 43A40: Character groups and dual objects

Group determinant symmetric group Lind-Lehmer constant Mahler measure


Pinner, Christopher. The integer group determinants for the symmetric group of degree four. Rocky Mountain J. Math. 49 (2019), no. 4, 1293--1305. doi:10.1216/RMJ-2019-49-4-1293.

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