The Normalizer Property for Integral Group Rings of a Class of Complete Monomial Groups

Abstract

Let G = H≀S _m be the natural wreath product of H by S _m , where H is a finite 2-closed group and S _m is the symmetric group of degree m. It is shown that the normalizer property holds for G.

Key Words:

• Integral group ring
• The normalizer property
• Trivial central unit

2010 Mathematics Subject Classification:

• 20C05
• 16S34
• 20C10

ACKNOWLEDGMENTS

The authors would like to thank the referee for his/her carefully reading the manuscript and especially for valuable suggestions making the revised version more readable.

The work was partially Supported by the National Natural Science Foundation of China (Grant No. 11171169; 11071155) and the Doctorial Foundation of Shandong Province(Grant No. BS2012SF003).

Notes

Communicated by I. Shestakov.