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Journal of the London Mathematical Society 2006 74(3):566-582; doi:10.1112/S0024610706023106
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© The London Mathematical Society

Finite Axiomatization of Finite Soluble Groups

John S. Wilson

University College Oxford OX1 4BH, United Kingdom wilsonjs{at}maths.ox.ac.uk

Received 17 October 2005.

It is proved that the finite soluble groups can be characterized among finite groups by a first-order sentence, namely, the sentence that asserts that no non-trivial element g is a product of 56 commutators [x, y] with entries x, y conjugate to g.


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