H.S. Ndakwo , M.A. Umar , A.M. Yau , Application of Character Theory of Finite Group, Research Journal of Applied Sciences, Volume 3,Issue 1, 2008, Pages 88-89, ISSN 1815-932x, rjasci.2008.88.89, (https://makhillpublications.co/view-article.php?doi=rjasci.2008.88.89) Abstract: One of the most celebrated applications of character theory to pure group theory is Burnside’s theorem which states that a group with order divisible by at most two primes is solvable. The proof of this theorem depends on the properties of algebraic integers. Keywords: Pure group;prime;solvable;algebraic integers;character theory;burnside’s theorem;celebrated