Burnside-Brauer Theorem for Table Algebras

In the character theory of finite groups the Burnside-Brauer Theorem is a well-known result which deals with products of characters in finite groups. In this paper, we first define the character products for table algebras and then by observing the relationship between the characters of a table algebra and the characters of its quotient, we provide a condition in which the products of characters of table algebras are characters. As a main result we state and prove the Burnside-Brauer Theorem on finite groups for table algebras.