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Finitely presented groups of Fibonacci type. part II

Published online by Cambridge University Press:  09 April 2009

Colin M. Campbell
Affiliation:
The Mathematical Institute University of St. AndrewsSt. Andrews KY16 9SS, Scotland
Edmund F. Robertson
Affiliation:
The Mathematical Institute University of St. AndrewsSt. Andrews KY16 9SS, Scotland
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Abstract

A class of cyclically presented groups with n generators and n Fibonacci type relations is discussed. Conditions are given for these groups to be finite and metacyclic. With these conditions the presentations are reduced to the standard form for metacyclic groups with trivial Schur multiplicator. This enables certain ismorphisms between the groups to be found.

Subject classification (Amer. Math. Soc. (MOS) 1970): 20 F 05.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1979

References

Beyl, F. R. (1973), ‘The Schur multiplicator of metacyclic groups’, Proc. Amer. Math. Soc. 40, 413418.CrossRefGoogle Scholar
Campbell, C. M. and Robertson, E. F. (1975a), ‘On metacyclic Fibonacci groups’, Proc. Edinburgh Math. Soc. 19, 253256.CrossRefGoogle Scholar
Campbell, C. M. and Robertson, E. F. (1975b), ‘On a class of finitely presented groups of Fibonacci type’, J. London Math. Soc. 11, 249255.CrossRefGoogle Scholar
Chalk, C. P. and Johnson, D. L. (1977), ‘The Fibonacci groups II’, Proc. Roy. Soc. Edinburgh 77A, 7986.CrossRefGoogle Scholar
Johnson, D. L. (1976), Presentations of groups (Cambridge University Press, Cambridge).Google Scholar
Johnson, D. L., Wamsley, J. W. and Wright, D. (1974), ‘The Fibonacci groups’, Proc. London Math. soc. 29, 577592.CrossRefGoogle Scholar
Lyndon, R. C. and Schupp, P. E. (1977), combinatorial group theory (Springer, Berlin).Google Scholar
Zassenhaus, H. (1958), The theory of groups (Chelsea, New York, 2nd ed.).Google Scholar
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