Dihedral Groups as Epimorphic Images of Some Fibonacci Groups

Abdullahi Umar, Bashir Ali

Abstract


The Fibonacci groups are defined by the presentation where ,  and all subscripts are assumed to be reduced modulo . In this paper we give an alternative proof that for , ,  and  are all infinite by establishing a morphism (or group homomorphism) onto the dihedral group  for all .


Keywords


Group; Fibonacci group; Dihedral group; (homo) Morphism.

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References


CAMPBELL, C.M., DOOSTIE, H. and ROBERTSON, E.F. 2004. On the Fibonacci Length of Powers of Dihedral Groups. Applications of Fibonacci Numbers 9, Ed. F.T. Howard, Kluwer, Dordrecht, 69-85.

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CONWAY, J.H. 1965. Solution of Advanced Problem 5327. American Mathematical Monthly 72(8): 915.

GALLIAN, J.A. 1998. Contemporary Abstract Algebra, Houghton Mifflin, Boston/New York.

THOMAS, R.M. 1991. The Fibonacci groups revisited. In Proceedings of Groups - St Andrews 1989, Volume 2 (London Math. Soc. Lecture Note Series 160, Cambridge University Press, 1991). (Eds.) CAMPBELL, C.M. and ROBERTSON, E.F. 445-454.




DOI: http://dx.doi.org/10.24200/squjs.vol18iss0pp54-59

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