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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 .
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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.
- CAMPBELL, C.M., ROBERTSON, E.F. and THOMAS, R.M. 1992. Fibonacci Groups and Semigroups. Technical Report CSD-50, Department of Computing Studies, University of Leicester.
- 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.
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.
CAMPBELL, C.M., ROBERTSON, E.F. and THOMAS, R.M. 1992. Fibonacci Groups and Semigroups. Technical Report CSD-50, Department of Computing Studies, University of Leicester.
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.