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Perfect McLain groups are superperfect

Published online by Cambridge University Press:  17 April 2009

A. J. Berrick  and
R. G. Downey
A. J. Berrick
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge 0511, Singapore.
R. G. Downey
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge 0511, Singapore.
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It is shown that if a McLain group is perfect, then it is super-perfect. The proof involves demonstrating that any dense linearly ordered set has the apparently stronger property of being superdense.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 2 , April 1984 , pp. 249 - 257
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Berrick, A.J., An approach to algebraic k-theory (Pitman Research Notes in Mathematics, 56. Pitman, London, 1982).Google Scholar
[2]Berrick, A.J., “Group extensions and their trivialisation”, submitted.Google Scholar
[3]Milnor, John, Introduction to algebraic K-theory (Annals of Mathematical Studies, 72. Princeton University Press, Princeton, 1971).Google Scholar
[4]Robinson, Derek J.S., Finiteness conditions and generalized soluble groups, Part II (Ergebnisse der Mathematik und ihrer Grenzgebiete, 63. Springer-Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar