The Tits Alternative for Cat(0) Cubical Complexes

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The Tits Alternative for Cat(0) Cubical Complexes

We prove a Tits alternative theorem for groups acting on CAT(0) cubical complexes. Namely, suppose that G is a group for which there is a bound on the orders of its finite subgroups. We prove that if G acts properly on a finitedimensional CAT(0) cubical complex, then either G contains a free subgroup of rank 2 or G is finitely generated and virtually abelian. In particular the above conclusion ...

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We shall say that the Tits Alternative holds for a class of groups if each group in the class is either solvable by ...nite (that is, contains a solvable normal subgroup of ...nite index) or contains a free subgroup of rank at least 2. Free groups of rank 2 contain free subgroups of countable rank, so in the second case there will be of free subgroups of all ...nite ranks. The Tits Alternative ...

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ژورنال

عنوان ژورنال: Bulletin of the London Mathematical Society

سال: 2005

ISSN: 0024-6093

DOI: 10.1112/s002460930500456x