Abstract
In this paper and a sequel, we study a group which is the quotient of a free oduct of groups by the normal closure of a single word that is contained in a subgroup which has the form of a free product of two cyclic groups.
We use known properties of generalised triangle groups, together with detailed analysis of pictures and of words in free monoids, to prove a number of results such as a Freiheitssatz and the existence of Mayer-Vietoris sequences for such groups under suitable hypotheses. The results eneralise those in an earlier article of the second author and Shwartz
We use known properties of generalised triangle groups, together with detailed analysis of pictures and of words in free monoids, to prove a number of results such as a Freiheitssatz and the existence of Mayer-Vietoris sequences for such groups under suitable hypotheses. The results eneralise those in an earlier article of the second author and Shwartz
| Original language | English |
|---|---|
| Pages (from-to) | 1138-1154 |
| Number of pages | 16 |
| Journal | Communications in Algebra |
| Volume | 46 |
| Issue number | 3 |
| Early online date | 11 Aug 2017 |
| DOIs | |
| Publication status | E-pub ahead of print - 11 Aug 2017 |
Keywords
- One-relator group
- generalised triangle groups
- Pictures
ASJC Scopus subject areas
- Mathematics(all)