Tits alternative

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In mathematics, the Tits alternative, named for Jacques Tits, is an important theorem about the structure of finitely generated linear groups.

Statement[edit]

It states that every such group is either virtually solvable (i.e. has a solvable subgroup of finite index), or it contains a subgroup isomorphic to the free group on two generators.

Generalization[edit]

In geometric group theory, a group G is said to satisfy the Tits alternative if for every subgroup H of G either H is virtually solvable or H contains a nonabelian free subgroup (in some versions of the definition this condition is only required to be satisfied for all finitely generated subgroups of G).

References[edit]