FREE SUBGROUPS OF THE GROUP OF INFINITE UNITRIANGULAR MATRICES
Waldemar Hołubowski · International Journal of Algebra and Computation · 2003
In this note we give simple explicit examples of free subgroups of rank 2 in the group of infinite upper unitriangular matrices over integers. The proofs that the given subgroup is free are elementary. Using canonical projections mod p (p — any odd prime) we obtain also free subgroups in the group of finite state automata on alphabet of size p, extending results of Aleshin [1], Brunner–Sidki [2] and Olijnyk–Sushchansky [8, 9] in this direction. As application, we give the simple proofs of two classical results on free groups.