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Free Fibonacci algebras

Published online by Cambridge University Press:  17 April 2009

D.L. Jonnson  and
A.C. Kim
D.L. Jonnson
Affiliation:
Mathematics Department, University of Nottingham, Nottingham NG7 2RD, England
A.C. Kim
Affiliation:
Mathematics DepartmentPusan National UniversityPusanKorea 607
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Abstract

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Fibonacci varieties were introduced by one of us in 1978 and a natural generalisation was studied shortly afterwards. We carry this investigation one stage further by giving a description of the free objects in these varieties. This is done in terms of the n-abelian groups of Levi.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 2 , October 1989 , pp. 235 - 241
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Alperin, J. L., ‘A classification of n-abelian groups’, Canad. J. Math. 21 (1969), 1238–1244.CrossRefGoogle Scholar
[2]Johnson, D. L., Wamsley, J. W. and Wright, D., ‘The Fibonacci groups’, Proc. London Math. Soc. (3) 19 (1974), 577–594.CrossRefGoogle Scholar
[3]Kim, Ann Chi, ‘Fibonacci varieties’, 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
[5]Levi, F., ‘Notes on group theory’, J. Indian Math. Soc. 8 (1944), 1–7.Google Scholar