Abstract:Abstract. Following Vinberg, we find the criterions for a subgroup generated by reflections Γ ⊂ SL ± (n + 1, R) and its finiteindex subgroups to be definable over A where A is an integrally closed Noetherian ring in the field R. We apply the criterions for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the n-dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to SL ± (n + 1, Z). Finall… Show more
Motivated by a question of Stover, we discuss an example of a Zariski-dense finitely generated subgroup of
S
L
5
(
Z
)
\mathrm {SL}_5(\mathbb {Z})
that is not finitely presented.
Motivated by a question of Stover, we discuss an example of a Zariski-dense finitely generated subgroup of
S
L
5
(
Z
)
\mathrm {SL}_5(\mathbb {Z})
that is not finitely presented.
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