Nonvanishing Elements in Table Algebras

Abstract

It is proved that nonvanishing elements of a commutative nilpotent table algebra must be linear, which generalizes the known result on the nonvanishing elements of a finite nilpotent group. Other results on nonvanishing elements of finite groups are generalized to the context of a commutative table algebra whose dual is also a commutative table algebra.

Key Words:

• Commutative table algebras
• Dual C-algebras
• Nilpotent table algebras
• Nonvanishing elements

2000 Mathematics Subject Classification:

• 20C15
• 20C20

ACKNOWLEDGMENT

The work was done during the visit of the second author at Northern Illinois University from February 2009 to January 2010. He appreciates the hospitality of the first author and the Department of Mathematical Sciences of Northern Illinois University. The work of the second author is supported by the National Science Foundation of China (No. 11001094), China Scholarship Council and The Key Project of Chinese Ministry of Education, No. 108099.

Notes

Communicated by Q. Wu.