Multiplicative Jordan decomposition in group rings and p-groups with all noncyclic subgroups normal

JOURNAL OF ALGEBRA

卷:371

Article

Liu, Chia-Hsin

关键词: Integral group rings;    Unit group;    Semisimple element;    Nilpotent element;    Jordan decomposition;    Noncyclic subgroup;    2-Group;    p-Group;   

DOI  :  10.1016/j.jalgebra.2012.07.010

来源: Elsevier

【 摘 要 】

Let p be a prime and let G be a finite p-group. We show that if the integral group ring Zinverted right perpendicularGinverted left perpendicular satisfies the multiplicative Jordan decomposition property, then every noncyclic subgroup of G is normal. This is used to simplify the work of Hales. Passi and Wilson on the classification of integral group rings of finite 2-groups with the multiplicative Jordan decomposition property. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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