nLab Tits alternative

Statement

A finitely generated linear group over a field has either

• a solvable subgroup of finite index,

• a subgroup which is a free group on two generators.

(due to Tits 1972)

This generalizes to hyperbolic groups and some other prominent classes.

References

The original article:

• Jacques Tits: Free subgroups in linear groups, Journal of Algebra 20 2 (1972) 250–270 [doi:10.1016/0021-8693(72)90058-0]

See also:

• Wikipedia: Tits alternative