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More Fibonacci varieties

Published online by Cambridge University Press:  17 April 2009

Ann Chi Kim ,
B.H. Neumann  and
A.H. Rhemtulla
Ann Chi Kim
Affiliation:
Department of Mathematics, Busan National University, Busan, Korea, 607
B.H. Neumann
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, PO Box 4, Canberra, ACT, Australia 2600, and Division of Mathematics and Statistics, Commonwealth Scientific and Industrial Research Organization, PO Box 1965, Canberra City, ACT, Australia 2601
A.H. Rhemtulla
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2GI.
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Abstract

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The Fibonacci varieties introduced by Ann Chi Kim, Bull. Austral. Math. Soc. 19 (1978), 191–196 (1979), are here generalised in an obvious way suggested by the work of D.L. Johnson, J.W. Wamsley, and D. Wright, Proc. London Math. Soc. (3) 29 (1974), 577–592. The underlying groups of algebras in these varieties are studied, and are shown to be abelian when the algebras are generated by a single element, and in general are found to be extensions of central subgroups by groups of finite exponent.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 3 , December 1980 , pp. 385 - 395
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Chalk, C.P. and Johnson, D.L., “The Fibonacci groups. II”, Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 79–86.CrossRefGoogle Scholar
[2]Johnson, D.L., “A note on the Fibonacci groups”, Israel J. Math. 17 (1974), 277–282.CrossRefGoogle Scholar
[3]Johnson, D.L., Wamsley, J.W., and Wright, D., “The Fibonacci groups”, Proc. London Math. Soc. (3) 19 (1974), 577–594.CrossRefGoogle Scholar
[4]Kim, Ann Chi, “Fibonacci varieties”, Bull. Austral. Math. Soc. 19 (1978), 191–196 (1979).CrossRefGoogle Scholar