Geodesic
The cyclically presented groups with relators $x_ix_{i+k}x_{i+l}$
Martin Edjvet1 ; Gerald Williams2
1University of Nottingham, UK
2Essex University, Colchester, UK
Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 759-775

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DOI

Continuing Cavicchioli, Repovš, and Spaggiari’s investigations into the cyclic presentations 〈x1​, ... , xn​∣xi​xi+k​xi+l​=1(1≤i≤n)〉 we determine when they are aspherical and when they define finite groups; in these cases we describe the groups’ structures. In many cases we show that if the group is infinite then it contains a non-abelian free subgroup.
DOI : 10.4171/ggd/104
Classification : 20-XX, 00-XX
Mots-clés : Cyclically presented group, asphericity

Martin Edjvet  1   ; Gerald Williams  2

1 University of Nottingham, UK
2 Essex University, Colchester, UK 
Martin Edjvet; Gerald Williams. The cyclically presented groups with relators $x_ix_{i+k}x_{i+l}$. Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 759-775. doi: 10.4171/ggd/104
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     title = {The cyclically presented groups with relators $x_ix_{i+k}x_{i+l}$},
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     pages = {759--775},
     year = {2010},
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     number = {4},
     doi = {10.4171/ggd/104},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/104/}
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