Let G be a finite group, N (sic) G a normal subgroup, p a prime, K = F(P)k a finite splitting field of characteristic p for G and n := exp(G/N). We prove that L := F (p)kn is a splitting field for N, using the action of the Galois group of the field extension K subset of L on the irreducible representations of N. As F-p is a splitting field for the symmetric group S-n we get as a corollary that F(p)2 is a splitting field for the alternating group An
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