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Stability of nilpotent groups of class 2 and prime exponent

Published online by Cambridge University Press:  12 March 2014

Alan H. Mekler
Alan H. Mekler*
Affiliation:
University of Toronto, Toronto, Canada
*
Simon Fraser University, Burnaby, British Columbia, Canada
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Abstract

Let p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M.

Theorem. There are nilpotent groups of class 2 and exponent p in all stability classes.

Theorem. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 4 , December 1981 , pp. 781 - 788
Copyright
Copyright © Association for Symbolic Logic 1981

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References

REFERENCES

[1]Baldwin, J. T. and Saxl, Jan, Logical stability in group theory, Journal of the Australian Mathematical Society (Series A), vol. 21 (1976), pp. 267–276.CrossRefGoogle Scholar
[2]Baur, W., Cherlin, G. and Macintyre, A., On totally categorical groups and rings, Journal of Algebra, vol. 57 (1979), pp. 407–440.CrossRefGoogle Scholar
[3]Belegradek, O. V., An example of a stable but not superstable group of bounded exponent, Notices of the American Mathematical Society, vol. 25 (1978), p. A–360, abstract 78T-E28.Google Scholar
[4]Keisler, H. J., Fundamentals of model theory, Handbook of mathematical logic (Barwise, Jon, Editor), North-Holland, Amsterdam, 1977, pp. 47–103.CrossRefGoogle Scholar
[5]MacHenry, T., The tensor product and the second nilpotent product of groups, Mathematische Zeitschrift, vol. 73 (1960), pp. 175–188.CrossRefGoogle Scholar