Tits alternative

Tits alternative

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

In geometric group theory, a class of groups is said to satisfy the Tits alternative if every group in the class is either virtually solvable or contains a nonabelian free subgroup.

References

*cite journal|last = Tits|first = J.|title = Free subgroups in linear groups|journal = J. Algebra|volume = 20|date = 1972|pages = 250–270|doi = 10.1016/0021-8693(72)90058-0
*cite journal|last = Bestvina|first = Mladen|coauthors = Feighn, Mark; Handel, Michael|title = The Tits alternative for Out("Fn") I: Dynamics of exponentially-growing automorphisms|journal = Annals of Mathematics|volume = 151|date = 2000|pages = 517–623|url = http://arxiv.org/pdf/math/9712217|doi = 10.2307/121043


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