The Normalizer Property for Integral Group Rings of Some Finite Nilpotent-by-Nilpotent Groups

Abstract

In this article, it is shown that the normalizer property holds for the following two kinds of finite nilpotent-by-nilpotent groups: (1) G = NwrH is the standard wreath product of N by H, where N is a finite nilpotent group and H is a finite abelian 2-group; (2) G is a finite group having a normal nilpotent subgroup N such that the integral group ring ℤ(G/N) has only trivial units. Our results generalize a result of Yuanlin Li and extend some ones obtained by Juriaans, Miranda, and Robério.

Key Words:

• Integral group rings
• The normalizer property
• Trivial units
• Wreath products

2010 Mathematics Subject Classification:

• 20C05
• 16U60
• 20C10

ACKNOWLEDGMENT

Supported by NSF of China (Grant No. 11171169, 11071155) and NSF of Shandong (Grant No. Y2008A03).

Notes

Communicated by S. Sehgal.