Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-19T17:24:02.858Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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