The Torsion Unit of the Integral Ring of the Direct Product of the Symmetric Group S5 and the Cyclic Group C3

Hong Yi WU, Jin Ke HAI

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 405-414.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 405-414. DOI: 10.12386/A2022sxxb0032

The Torsion Unit of the Integral Ring of the Direct Product of the Symmetric Group S5 and the Cyclic Group C3

  • Hong Yi WU, Jin Ke HAI
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Abstract

In this paper, we investigate the normalized torsion units of the integral group ring of the direct product of the symmetric group S5 and the cyclic group C3. As a consequence, we confirm the Zassenhaus's conjecture about this group.

Key words

integral group ring / torsion unit / the partial augmentation / Zassenhaus's conjecture

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Hong Yi WU, Jin Ke HAI. The Torsion Unit of the Integral Ring of the Direct Product of the Symmetric Group S5 and the Cyclic Group C3. Acta Mathematica Sinica, Chinese Series, 2022, 65(3): 405-414 https://doi.org/10.12386/A2022sxxb0032

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