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The unitary group over the integers of a quaternion algebra
Authors:Chan-nan Chang
Affiliation:Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01002 USA
Abstract:Let L be a lattice over the integers of a quaternion algebra with center K which is a B-adic field. Then the unitary group U(L) equals its own commutator subgroup Ω(L) and is generated by the unitary transvections and quasitransvections contained in it. Let g be a tableau, U(g), U+(g), Ω(g), T(g) be the corresponding congruence subgroups of order g. Then U(g)U+(g) ? Xi = 1τZ2, and Ω(g) = T(g) (the subgroup generated by the unitary transvections and quasitransvections with order ≤ g). Let G be a subgroup of U(L) with o(G) = g, then G is normal in U(L) if and only if U(g) ? G ? T(g).
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