A Geometric Invariant for Metabelian Pro-p Groups |
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Authors: | King Jeremy D. |
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Affiliation: | Tonbridge School Tonbridge, Kent TN9 1JP |
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Abstract: | In [2] Bieri and Strebel introduced a geometric invariant forfinitely generated abstract metabelian groups that determineswhich groups are finitely presented. For a valuable survey oftheir results, see [6]; we recall the definition briefly inSection 4. We shall introduce a similar invariant for pro-pgroups. Let F be the algebraic closure of Fp and U be the formal powerseries algebra F[T], with group of units Ux. Let Q be a finitelygenerated abelian pro-p group. We write Zp[Q] for the completedgroup algebra of Q over Zp. Let T(Q) be the abelian group Hom(Q,Ux) of continuous homomorphisms from Q to Ux. We write 1 forthe trivial homomorphism. Each vT(Q) extends to a unique continuousalgebra homomorphism from Zp[Q]to U. |
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