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Fibonacci varieties

Published online by Cambridge University Press:  17 April 2009

Ann Chi Kim
Ann Chi Kim
Affiliation:
Department of Mathematics, Busan National University, Busan, Korea.
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Abstract

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This is a report on a family of varieties of algebraic systems that are groups with an additional unary operation satisfying certain laws. The study was inspired by the theory of Fibonacci groups, and the free one-generator algebras of our varieties turn out to have, in fact, the abelianized Fibonnaci groups as their underlying groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 2 , October 1978 , pp. 191 - 196
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Brunner, A.M., “Fibonacci sequences and group theory” (PhD thesis, Australian National University, Canberra, 1973). See also: Abstract, Bull. Austral. Math. Soc. 9 (1973), 473–474.CrossRefGoogle Scholar
[2]Campbell, C.M. and Robertson, E.F., “Deficiency zero groups involving Fibonacci and Lucas numbers”, Proc. Roy. Soc. Edinburgh Sect. A (to appear).Google Scholar
[3]Conway, J.H., “Advanced problem 5327”, Amer. Math. Monthly 72 (1965), 915.Google Scholar
[4]Johnson, D.L., Presentations of groups (London Mathematical Society Lecture Notes Series, 22. Cambridge University Press, Cambridge, London, New York, Melbourne, 1976).Google Scholar
[5]Johnson, D.L., Wamsley, J.W., and Wright, D., “The Fibonacci groups”, Proc. London Math. Soc. (3) 29 (1974), 577–592.CrossRefGoogle Scholar
[6]Lyndon, Roger C., “On a family of infinite groups introduced by Conway”, unpublished manuscript.Google Scholar
[7]Neumann, B.H., “The reflection principle”, Math. Chronicle 5 (1976), 1–7.Google Scholar
[8] Various Authors, “Generators and relations for cyclic groups” (Solution to advanced problem 5327, see [3] above), Amer. Math. Monthly 74 (1967), 91–93.Google Scholar