Dihedral groups as epimorphic images of some fibonacci groups

الملخص EN

The Fibonacci groups are defined by the presentation F (r, n) = A1, a2,…,an : a1a2…ar = ar+1,a2a3…ar+1 = ar+2,…, ana1…-ar-1 = ar),where r > 0, n > 0 and all subscripts are assumed to be reduced modulo n .

In this paper we give an alternative proof that for r > 0, F(2r, 4r + 2), F(4r + 3, 8r + 8) and F(4r + 5, 8r +12) are all infinite by establishing a morphism (or group homomorphism) onto the dihedral group Dn for all n > 2.1