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Periodic Fibonacci algebras

Published online by Cambridge University Press:  20 January 2009

D. L. Johnson  and
A. C. Kim
D. L. Johnson
Affiliation:
Mathematics DepartmentUniversity of NottinghamNottingham NG7 2RDEngland
A. C. Kim
Affiliation:
Mathematics DepartmentBusan National UniversityBusan 607, Korea
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Abstract

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Fibonacci algebras are groups equipped with an extra unary operation φ that satisfies a Fibonacci-type law. We described in an earlier paper the free objects in the resulting varieties, and here we do the same in the case when φ is assumed to be periodic. They turn out to be central extensions of Burnside groups with finite kernels whose orders can be expressed in terms of the resultants of certain polynomials.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 2 , June 1992 , pp. 169 - 172
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Johnson, D. L., A note on the Fibonacci groups, Israel J. Math. 17 (1974), 277–282.CrossRefGoogle Scholar
2.Johnson, D. L. and Kim, Ann Chi, Free Fibonacci Algebras, Bull. Austral. Math. Soc. 40, (1989), 235–241.CrossRefGoogle Scholar
3.Kim, Ann Chi, Fibonacci variaties, Bull. Austral. Math. Soc. 19 (1978), 191–196.CrossRefGoogle Scholar
4.Kim, Ann Chi, Neumann, B. H. and Rhemtulla, A. H., More Fibonacci varieties, Bull. Austral. Math. Soc. 22 (1980), 385–395.CrossRefGoogle Scholar