This paper is devoted to a study of groups defined by the presentation G=<a,b,c | a^b=a^r,b^c=b^s,c^a=c^t> (r,s,t integers). It is proved that G''<=Z(G) and that if r,s and t are all <> -3,-1, then G is finite and its order divides |(r-1,s-1)(s-1,t-1)(t-1,r-1)hkj| where h=r^(|s-1|)-1, k=s^(|t-1|)-1 and j=t^(|r-1|)-1.
Gruppi fattorizzati da sottogruppi ciclici.
JABARA, Enrico
2009-01-01
Abstract
This paper is devoted to a study of groups defined by the presentation G= (r,s,t integers). It is proved that G''<=Z(G) and that if r,s and t are all <> -3,-1, then G is finite and its order divides |(r-1,s-1)(s-1,t-1)(t-1,r-1)hkj| where h=r^(|s-1|)-1, k=s^(|t-1|)-1 and j=t^(|r-1|)-1.File in questo prodotto:
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