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The SQ-universality of some finitely presented groups

Published online by Cambridge University Press:  09 April 2009

Peter M. Neumann
Peter M. Neumann
Affiliation:
Queen' CollegeOxford OX1 4AWEngland
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Following a suggestion of G. Higman we say that the group G is SQ-universal if every countable group is embeddable in some factor group of G. It is a well-known theorem of G. Higman, B. H. Neumann and Hanna Neumann that the free group of rank 2 is sq-universal in this sense. Several different proofs are now available (see, for example, [1] or [9]). It is my intention to prove the LEmma. If H is a subgroup of finite index in a group G, then G is SQ-universal if and only if H is SQ-universal.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 1 , August 1973 , pp. 1 - 6
Copyright
Copyright © Australian Mathematical Society 1973

References

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