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The last of the Fibonacci groups

Published online by Cambridge University Press:  14 November 2011

George Havas
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra
J. S. Richardson
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria
Leon S. Sterling
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra

Synopsis

All the Fibonacci groups in the family F(2, n) have been either fully identified or determined to be infinite, bar one, namely F(2, 9). Using computer-aided techniques it is shown that F(2, 9) has a quotient of order 152.5741, and an explicit matrix representation for a quotient of order 152.518 is given. This strongly suggests that F(2, 9) is infinite, but no proof of such a claim is available.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1979

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