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{\bf J. Bagherian and  A. Rahnamai Barghi}
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{\bf Burnside-Brauer Theorem for Table Algebras}
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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.

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