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Amalgamated sums of groups

Published online by Cambridge University Press:  20 January 2009

J. M. Corson
J. M. Corson
Affiliation:
Department of Mathematics University of Alabama Box 870350 Tuscaloosa, AL 35487–0350 U.S.A. E-mail address: [email protected]
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Abstract

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Groups called amalgamated sums that arise as inductive limits of systems of groups and injective homomorphisms are studied. The problem is to find conditions under which the groups in the system do not collapse in the limit. Such a condition is given by J. Tits when certain subsystems are associated to buildings. This condition can be phrased to apply to certain systems of abstract groups and injective homomorphisms. It is shown to imply that no collapse occurs in the limit in a strong sense; namely the natural homomorphism of the amalgamated sum of any subsystem into the amalgamated sum of the full system is injective. This answers a question of S. J. Pride.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 3 , October 1996 , pp. 561 - 570
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

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