# Product of Irreducible Characters

• Published : 2002.09.01

#### Abstract

In this paper we prove that tile property of product irreducible characters is, if $\Phi$$\in$$\textit{Irr(H)}$ and $\Theta$$\in$$\textit{Irr(K)}$ are faithful, then $\Phi$$\times\theta$ is faithful if and only if │$\textit{Z(H)}$│ and │$\textit{Z(K)}$│ are relative primes where G=$\textit{H}\times\textit{K}$.

#### References

1. Proc. London Math. Soc. v.2 no.2 On groups of order $P^aQ^b$ II Burnside, W
2. Theory of Groups of Finite Order 2nd Burnside, W
3. Representations and characters of Finite Groups Collins, M.J
4. Methods of Representations Theory I Curtis, C.W;Reiner, I
5. Group representation theory Dornhoff, L
6. Math. Z. v.113 A group theoretic proof of the $p^aq^b$ theorem for odd primes Goldschmidt, D.M
7. Character Theory of Finite Group Isaacs, M
8. Representations and Characters of Groups James, G;Liebeck, M
9. Osaka J. Math. v.10 Solvability of groups of order $2^ap^b$ Matsuyama, H
10. Group Theory I Suzuki, M
11. Group Theory II Suzuki, M