TY - INPR
A1 - Madlener, Klaus
A1 - Friedrich, Otto
T1 - Some Applications Of Prefix-Rewriting In Monoids, Groups, And Rings
N2 - Rewriting techniques have been applied successfully to various areas of symbolic computation. Here we consider the notion of prefix-rewriting and give a survey on its applications to the subgroup problem in combinatorial group theory. We will see that for certain classes of finitely presented groups finitely generated subgroups can be described through convergent prefix-rewriting systems, which can be obtained from a presentation of the group considered and a set of generators for the subgroup through a specialized Knuth-Bendix style completion procedure. In many instances a finite presentation for the subgroup considered can be constructed from such a convergent prefix-rewriting system, thus solving the subgroup presentation problem. Finally we will see that the classical procedures for computing Nielsen reduced sets of generators for a finitely generated subgroup of a free group and the Todd-Coxeter coset enumeration can be interpreted as particular instances of prefix-completion. Further, both procedures are closely related to the computation of prefix Gr"obner bases for right ideals in free group rings.
T3 - Reports on Computer Algebra (ZCA Report) - 22
KW - monoid- and group-presentations
KW - subgroup problem
KW - subgroup presentation problem
KW - prefix-rewriting
KW - confluence
KW - coset enumeration
KW - GrÃ¶bner base
Y1 - 1998
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/792
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-7612
ER -