Multiplicative Jordan decomposition in group rings with a Wedderburn component of degree 3

Chia Hsin Liu, D. S. Passman

研究成果: 雜誌貢獻文章

2 引文 斯高帕斯(Scopus)

摘要

If G is a finite group whose integral group ring Z[G] has the multiplicative Jordan decomposition property, then it is known that all Wedderburn components of the rational group ring Q[G] have degree at most 3. While degree 3 components can occur, we prove here that if they do, then certain central units in Z[G] cannot exist. With this, we are able to greatly simplify the argument that characterizes those 3-groups with integral group ring having MJD. Furthermore, we show that if G is a nonabelian semidirect product of the form Cp⋊C3k, with prime p > 7 and with the cyclic 3-group acting like a group of order 3, then Z[G] does not have MJD.

原文英語
頁(從 - 到)203-218
頁數16
期刊Journal of Algebra
388
DOIs
出版狀態已發佈 - 2013 八月 15

ASJC Scopus subject areas

  • Algebra and Number Theory

指紋 深入研究「Multiplicative Jordan decomposition in group rings with a Wedderburn component of degree 3」主題。共同形成了獨特的指紋。

  • 引用此