We consider three infinite families of cyclic presentations of groups, depending on a finite set of integers and having the same polynomial. Then we prove that the corresponding groups with the same parameters are isomorphic, and that the groups are almost all infinite. Finally, we completely compute the maximal Abelian quotients of such groups, and show that their HNN extensions are high-dimensional knot groups. Our results contain as particular cases the main theorems obtained in two nice articles: Johnson et al. (1999) and Havas et al. (2001).

Certain cyclically presented groups with the same polynomial / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 34:(2006), pp. 2733-2744.

Certain cyclically presented groups with the same polynomial

CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2006

Abstract

We consider three infinite families of cyclic presentations of groups, depending on a finite set of integers and having the same polynomial. Then we prove that the corresponding groups with the same parameters are isomorphic, and that the groups are almost all infinite. Finally, we completely compute the maximal Abelian quotients of such groups, and show that their HNN extensions are high-dimensional knot groups. Our results contain as particular cases the main theorems obtained in two nice articles: Johnson et al. (1999) and Havas et al. (2001).
34
2733
2744
Certain cyclically presented groups with the same polynomial / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 34:(2006), pp. 2733-2744.
Cavicchioli, Alberto; Spaggiari, Fulvia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/309969
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