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On the structure of certain arithmetic subgroups of SL2()

Published online by Cambridge University Press:  24 October 2008

C. Maclachlan
C. Maclachlan
Affiliation:
Department of Mathematics, University of Aberdeen
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Extract

In [6], p. 80, Serre showed that the group SL2(Z[1/p]) is a free product of two copies of SL2(Z) amalgamated along a sub-group of index p + 1 in both components. This result was obtained from the structure theory of groups acting on trees and the construction of a tree on which SL2 over a field with discrete valuation acts in a natural way. This result can be extended to other SL2 examples. Using the above description, Serre [6] also gave presentations for the groups SL2(Z[1/p]) where p = 2, 3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 2 , March 1985 , pp. 211 - 217
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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