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On quotients of certain countable groups

Published online by Cambridge University Press:  17 April 2009

Stephen J. Pride
Stephen J. Pride
Affiliation:
Faculty of Mathematics, The Open University, Milton Keynes, England.
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Abstract

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A group A is said to be SQ-universal if every countable group is embeddable in some quotient of A. It is well-known that the number of non-isomorphic factor groups of a countable sp-universal group B is the power of the continuum. Since B has such an abundance of non-isomorphic quotients it is natural to ask what types of quotients B must have and what types B need not have. This note is concerned with these questions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 2 , April 1977 , pp. 225 - 228
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Neumann, Peter M., “The SQ-universality of some finitely presented groups”, J. Austral. Math. Soc. 16 (1973), 1–6.CrossRefGoogle Scholar
[2]Schupp, Paul E., “A survey of SQ-universality”, Conference on group theory, University of Wisconsin-Parkside, 1972, 183–188 (Lecture Notes in Mathematics, 319. Springer-Verlag, Berlin, Heidelberg, New York, 1973).Google Scholar
[3]Schupp, Paul E., “A survey of small cancellation theory”, Word problems: decision problems and the Burnside problem in group theory, 569–589 (Studies in Logic and the Foundations of Mathematics, 71. North-Holland, Amsterdam, London, 1973).Google Scholar