Rewriting Products of Group Elements

Let G be a group and let n be an integer greater than 1. An n-tuple $({\rm x\sb1,\dots, x\sb{n}})$ of elements of G is said to be rewriteable if there is a nontrivial permutation σ in Sym(n) such that {\rm x\sb1\dots x\sb{n} = x\sb{σ (1)}\dots x\sb{σ (n)}}. A subset $\{ {\rm x\sb1,\dots, x\sb{n}}\}$ of n elements of G is said to be rewriteable if there exist distinct permutations σ and $\tau$ in Sym(n) such that {\rm x\sb{σ (1)}\dots x\sb{σ (n)} = x\sb{\tau (1)}\dots x\sb{\tau (n)}}. The group G is totally n-rewriteable (where n $>$ 1), or has the property P $\sb{\rm n},$ if every n-tuple $({\rm x\sb1,\dots, x\sb{n}})$ of n elements of G is rewriteable. G is n-rewriteable, or has the property Q $\sb{\rm n},$ if every subset $\{ {\rm x\sb1,\dots, x\sb{n}}\}$ of n elements of G is rewriteable.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

1987

Author dc:creator

• Blyth, Russell David

• Mathematics

Identifier

(UMI)AAI8721590

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71252