作者：He; Guo; LIU; Yu; Lei; WANG; Ji; Ping;...extraspecialgroupextensionsymplecticautomorphism
摘要：Let G be an extension of Q by a direct sum of r copies of Q.(1) If G is abelian, then G is a direct sum of r + 1 copies of Q and Aut G = GL(r + 1, Q);(2) If G is non-abelian, then G is a direct product of an extraspecial Q-group E and m copies of Q, where E/ζ E is a linear space over Q with dimension 2 n and m + 2 n = r. Furthermore, let AutG’G be the normal subgroup of Aut G consisting of all elements of Aut G which act trivially on the derived subgroup G of G, and AutG/ζG,ζGG be the normal subgroup of Aut G consisting of all central automorphisms of G which also act trivially on the center ζ G of G. Then(i) The extension 1→ AutG’G→ Aut G→ Aut G’→ 1 is split;(ii)AutG’G/AutG/ζG,ζGG ≌ Sp(2 n, Q) ×(GL(m, Q) ■Q^(m);(iii) AutG/ζG,ζGG/Inn G≌ Q^(2 nm).
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