Diego Rattaggi

Publications (4)0 Total impact

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  Available from: ArXiv

  Article: On direct product subgroups of $\mathrm{SO}_3(\mathbb{R})$

  Diego Rattaggi
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  ABSTRACT: Let $G_1 \times G_2$ be a subgroup of $\mathrm{SO}_3(\mathbb{R})$ such that the two factors $G_1$ and $G_2$ are non-trivial groups. We show that if $G_1 \times G_2$ is not abelian, then one factor is the (abelian) group of order 2, and the other factor is non-abelian and contains an element of order 2. There exist finite and infinite such non-abelian subgroups.
  09/2006;
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  Available from: ArXiv

  Article: An incoherent simple group

  Diego Rattaggi
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  ABSTRACT: We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.
  08/2005;
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  Available from: ArXiv

  Article: Three amalgams with remarkable normal subgroup structures

  Diego Rattaggi
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  ABSTRACT: We construct three groups $\Lambda_1$, $\Lambda_2$, $\Lambda_3$, which can all be decomposed as amalgamated products $F_9 \ast_{F_{81}} F_{9}$ and have very few normal subgroups of finite or infinite index. Concretely, $\Lambda_1$ is a simple group, $\Lambda_2$ is not simple but has no non-trivial normal subgroup of infinite index, and $\Lambda_3$ is not simple but has no proper subgroup of finite index.
  07/2005;
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  Available from: arxiv.org

  Article: A finitely presented torsion-free simple group

  Diego Rattaggi
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  ABSTRACT: We construct a finitely presented torsion-free simple group $\Sigma_0$, acting cocompactly on a product of two regular trees. An infinite family of such groups has been introduced by Burger-Mozes ([2,4]). We refine their methods and get $\Sigma_0$ as an index 4 subgroup of a group $\Sigma < \mathrm{Aut}(\mathcal{T}_{12}) \times \mathrm{Aut}(\mathcal{T}_{8})$ presented by 10 generators and 24 short relations. For comparison, the smallest virtually simple group of [4, Theorem 6.4] needs more than 18000 relations, and the smallest simple group constructed in [4, Section 6.5] needs even more than 360000 relations in any finite presentation.
  12/2004;