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Free Products with Amalgamation and p-Adic Lie Groups

Published online by Cambridge University Press:  20 November 2018

D. D. Long
Affiliation:
Department of Mathematics University of California Santa Barbara, California 93106 U.S.A.
A. W. Reid
Affiliation:
Department of Mathematics University of Texas Austin, Texas 78712 U.S.A.
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Abstract

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Using the theory of $p$-adic Lie groups we give conditions for a finitely generated group to admit a splitting as a non-trivial free product with amalgamation. This can be viewed as an extension of a theorem of Bass.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Bass, H., Groups of integral representation type. Pacific J. Math. 86 (1980), 1551.Google Scholar
2. Bass, H., Finitely generated subgroups of GL2 . In: The Smith Conjecture, (eds. J.W.Morgan and H.Bass), Academic Press, Orlando, 1984, 127136.Google Scholar
3. Baumslag, G. and Shalen, P. B., Amalgamated products and finitely presented groups. Comment. Math. Helv. 65 (1990), 243254.Google Scholar
4. Culler, M. and Shalen, P. B., Bounded separating incompressible surfaces in knot manifolds. Invent. Math. 75 (1984), 537545.Google Scholar
5. Dixon, J. D., Du Sautoy, M. P. F., Mann, A. and Segal, D., Analytic pro-p Groups. L.M.S. Lecture Note Series 157, Cambridge Univ. Press, 1991.Google Scholar
6. Ihara, Y., On discrete subgroups of the two by two projective linear group over p-adic fields. J. Math. Soc. Japan 18 (1966), 219235.Google Scholar
7. Long, D. D., Maclachlan, C. and Reid, A. W., Splitting groups of signature (1, n). J. Algebra 185 (1996), 329341.Google Scholar
8. Rotman, J. J., An Introduction to the Theory of Groups. Allyn and Bacon Inc, 1984.Google Scholar
9. Serre, J.-P., Trees. Springer-Verlag, 1980.CrossRefGoogle Scholar
10. Serre, J.-P., Lie Algebras and Lie Groups. Lecture Notes in Math. 1500, Springer-Verlag, 1991.Google Scholar
11. Scott, G. P. and Wall, C. T. C., Topological methods in group theory. In: Homological Group Theory, L.M.S. Lecture Notes 36, 137–203, Cambridge Univ. Press, 1979.CrossRefGoogle Scholar
12. Shalen, P. B., Separating incompressible surfaces in 3-manifolds. Invent. Math. 52 (1979), 105126.Google Scholar
13. Thurston, W., The Geometry and Topology of 3-Manifolds. mimeographed lecture notes, Princeton University, 1977.Google Scholar
14. Vignéras, M-F., Arithmétique des algèbres de Quaternions. Lecture Notes in Math. 800, Springer Verlag, Berlin, 1980.CrossRefGoogle Scholar
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