id: 01060732
dt: j
an: 01060732
au: Brunner, A.M.; Sidki, Said
ti: The generation of $\text{GL}(n,{\bbfZ})$ by finite state automata.
so: Int. J. Algebra Comput. 8, No. 1, 127-139 (1998).
py: 1998
pu: World Scientific, Singapore
la: EN
cc:
ut: groups of automorphisms of one-rooted regular trees; finite state automata;
general linear groups; free groups
ci:
li: doi:10.1142/S0218196798000077
ab: The linear group $\text{GL}(n,{\bbfZ})$ is residually finite by virtue of
its action on the (one-rooted) regular $2^n$-ary coset tree for
${\bbfZ}^n$. In this paper we construct finite state automata which
effect this action. This shows that $\text{GL}(n,{\bbfZ})$ is
embeddable in the group of finite state automorphisms of the one-rooted
regular tree of valency $2^n$.
rv: A.M.Brunner (Kenosha)