Non-free two-generator subgroups of SL2(Q).

Farbman, S. Peter. "Non-free two-generator subgroups of SL2(Q).." Publicacions Matemàtiques 39.2 (1995): 379-391. <http://eudml.org/doc/41227>.

@article{Farbman1995,
abstract = {The question of whether two parabolic elements A, B of SL2(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| &lt; 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL2(C) will not be free.},
author = {Farbman, S. Peter},
journal = {Publicacions Matemàtiques},
keywords = {Grupos de Moebius; Familias de subgrupos; parabolic elements; free groups},
language = {eng},
number = {2},
pages = {379-391},
title = {Non-free two-generator subgroups of SL2(Q).},
url = {http://eudml.org/doc/41227},
volume = {39},
year = {1995},
}

TY - JOUR
AU - Farbman, S. Peter
TI - Non-free two-generator subgroups of SL2(Q).
JO - Publicacions Matemàtiques
PY - 1995
VL - 39
IS - 2
SP - 379
EP - 391
AB - The question of whether two parabolic elements A, B of SL2(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| &lt; 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL2(C) will not be free.
LA - eng
KW - Grupos de Moebius; Familias de subgrupos; parabolic elements; free groups
UR - http://eudml.org/doc/41227
ER -