The search session has expired. Please query the service again.
Displaying 261 –
280 of
664
We show that the class of groups which have monoid presentations by means of finite special -confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.
We show that the class of groups which
have monoid presentations by means of finite special
[λ]-confluent string-rewriting systems strictly contains the class of plain groups
(the groups which are free products of a finitely generated free
group and finitely many finite groups),
and that any group
which has an infinite cyclic central subgroup
can be presented by such a string-rewriting system if and only if it is the
direct product of an infinite cyclic group and a finite cyclic group.
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.
Currently displaying 261 –
280 of
664