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Finite splitting fields of normal subgroups

Authors:	Email author" target="_blank">H?Meyer Email author

Institution:	(1) Lehrstuhl IV für Mathematik, Universität Bayreuth, D-95440 Bayreuth, Germany

Abstract:	Let G be a finite group, $N \triangleleft G$ a normal subgroup, p a prime, $K = \mathbb{F}_{p^{k}}$ a finite splitting field of characteristic p for G and $n := \exp (G/N).$ We prove that $L := \mathbb{F}_{p^{kn}}$ is a splitting field for N, using the action of the Galois group of the field extension $K \subset L$ on the irreducible representations of N. As $\mathbb{F}_{p}$ is a splitting field for the symmetric group S_n we get as a corollary that $\mathbb{F}_{p^2}$ is a splitting field for the alternating group A_n. Received: 31 July 2003

Keywords:	20C20 20C30
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