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

Publicacions Matemàtiques (1995)

- Volume: 39, Issue: 2, page 379-391
- ISSN: 0214-1493

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topFarbman, 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| < 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| < 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 -

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