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A group with very strange decomposition properties

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

M. J. Dunwoody  and
J. M. Jones
J. M. Jones
Affiliation:
Faculty of Mathematics University of Southampton Southampton, SO17 1BJ UK
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Abstract

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An example is given of a finitely generated group G for which G ≅ G*cG, where C is infinite cyclic.

MSC classification

Secondary: 20E08: Groups acting on trees 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20F05: Generators, relations, and presentations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 2 , October 1999 , pp. 185 - 190
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Dunwoody, M. J., ‘Inaccessible groups and protrees’, J. Pure Appl. Algebra 88 (1993), 63–78.CrossRefGoogle Scholar
[2]Dunwoody, M. J. and Jones, J. M., ‘A group with strange decomposition properties’, J. Group Theory 1 (1998), 301–305.Google Scholar
[3]Jones, J. M. T., ‘Direct products and the Hopf property’, J. Austral. Math. Soc. 17 (1974), 174–196.CrossRefGoogle Scholar
[4]Lyndon, R. C. and Schupp, P. E., Combinatorial group theory (Springer, Berlin, 1977).Google Scholar