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The Definability of the Commutator Subgroup in a Variety Generated by a Finite Group

Published online by Cambridge University Press:  20 November 2018

John Lawrence
John Lawrence*
Affiliation:
University of WaterlooWaterloo, Ontario N2L 3G1
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Abstract

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In a variety generated by a finite non-Abelian group, the commutator subgroup is not definable by a first-order formula.

Keywords

20A1520E1003B10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 505 - 507
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Lyndon, R.C., Equations in groups, Bol. Soc. Bras. Mat. 11 (1980), pp. 79–102.Google Scholar
2. Rogers, P., Smith, H., and Solitar, D., Tarski's problem for solvable groups, (preprint).Google Scholar
3. Scott, W.R., Group Theory, Prentice Hall (1960).Google Scholar