Normal series and character values in p-standard table algebras

ABSTRACT

We investigate the character values and structures of p-standard table algebras (A,B) with o(B) = p^N. If N≤3, then B has a complete normal series. If for every χ∈Irr(B), χ has at most p distinct classes of character values, and if either B has a complete normal series or p = 2, then B is an elementary abelian p-group.

KEYWORDS:

• p-Standard table algebras
• classes of character values
• complete normal series
• elementary abelian groups

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20C15
• 16K20
• 16W10

Acknowledgment

This work was done during the visit of Chen at Northern Illinois University from February to August 2016. He appreciates the hospitality of Professor Blau and the Department of Mathematical Sciences of Northern Illinois University.