对称群 S5与循环群 C3直积的整群环的挠单位

吴洪毅, 海进科

数学学报 ›› 2022, Vol. 65 ›› Issue (3) : 405-414.

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数学学报 ›› 2022, Vol. 65 ›› Issue (3) : 405-414. DOI: 10.12386/A2022sxxb0032
论文

对称群 S5与循环群 C3直积的整群环的挠单位

    吴洪毅, 海进科
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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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摘要

本文研究了五次对称群S5与三阶循环群C3直积的整群环的正规化挠单位.作为应用, 证明了S5×C3满足Zassenhaus猜想.

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.

关键词

整群环 / 挠单位 / 偏增广 / Zassenhaus猜想

Key words

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

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吴洪毅, 海进科. 对称群 S5与循环群 C3直积的整群环的挠单位. 数学学报, 2022, 65(3): 405-414 https://doi.org/10.12386/A2022sxxb0032
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

参考文献

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基金

基金项目:国家自然科学基金资助项目(11871292)
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