ASYMPTOTIC PROPERTIES OF ELEMENTS IN GROUP RINGS OF FINITE GROUPS

Abstract

A relation between algebraic degrees of eigenvalues of an element in the group ring Z G of a finite group G and their multiplicities is obtained. This result can be regarded as a theorem on asymptotic behavior of parameters in group rings of finite groups which is a parallel result of several well known theorems concerning the relationships of parameters in finite groups.

Keywords:

• Group ring
• Spectrum
• Algebraic degree
• 1991 Mathematics Subject Classification: 20C05.

ACKNOWLEDGMENTS

Research is partially supported by RFBR (grant # 99-01-00929). Research is also partially supported by a (CUHK) direct grant (2000/01) # 2060196.