FINITE AXIOMATIZATION OF FINITE SOLUBLE GROUPS

JOHN S. WILSON

doi:10.1112/S0024610706023106

Abstract

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 $g$.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Guralnick, R. Kantor, W. Kassabov, M. and Lubotzky, A. 2008. Presentations of finite simple groups: A quantitative approach. Journal of the American Mathematical Society, Vol. 21, Issue. 3, p. 711.

Zarrin, Mohammad 2009. On element-centralizers in finite groups. Archiv der Mathematik, Vol. 93, Issue. 6, p. 497.

Wilson, John S. 2009. First-order characterization of the radical of a finite group. The Journal of Symbolic Logic, Vol. 74, Issue. 4, p. 1429.

GOMAA, WALID 2010. DESCRIPTIVE COMPLEXITY OF FINITE ABELIAN GROUPS. International Journal of Algebra and Computation, Vol. 20, Issue. 08, p. 1087.

Abdollahi, A. Azad, A. Mohammadi Hassanabadi, A. and Zarrin, M. 2010. On the Clique Numbers of Non-commuting Graphs of Certain Groups. Algebra Colloquium, Vol. 17, Issue. 04, p. 611.

Guralnick, R.M. Kantor, W.M. Kassabov, M. and Lubotzky, A. 2011. Remarks on proficient groups. Journal of Algebra, Vol. 326, Issue. 1, p. 169.

GRUNEWALD, FRITZ KUNYAVSKII, BORIS and PLOTKIN, EUGENE 2013. CHARACTERIZATION OF SOLVABLE GROUPS AND SOLVABLE RADICAL. International Journal of Algebra and Computation, Vol. 23, Issue. 05, p. 1011.

Horváth, Gábor and Nehaniv, Chrystopher L. 2015. Length of polynomials over finite groups. Journal of Computer and System Sciences, Vol. 81, Issue. 8, p. 1614.

Bogley, William A. and Williams, Gerald 2016. Efficient finite groups arising in the study of relative asphericity. Mathematische Zeitschrift, Vol. 284, Issue. 1-2, p. 507.

Macpherson, Dugald 2018. Model theory of finite and pseudofinite groups. Archive for Mathematical Logic, Vol. 57, Issue. 1-2, p. 159.

CORNULIER, YVES and WILSON, JOHN S. 2020. FIRST-ORDER RECOGNIZABILITY IN FINITE AND PSEUDOFINITE GROUPS. The Journal of Symbolic Logic, Vol. 85, Issue. 2, p. 852.

Nies, Andre Segal, Dan and Tent, Katrin 2021. Finite axiomatizability for profinite groups. Proceedings of the London Mathematical Society, Vol. 123, Issue. 6, p. 597.

Martin, Benjamin 2024. Powers of commutators in linear algebraic groups. Proceedings of the Edinburgh Mathematical Society, Vol. 67, Issue. 3, p. 830.

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FINITE AXIOMATIZATION OF FINITE SOLUBLE GROUPS

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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FINITE AXIOMATIZATION OF FINITE SOLUBLE GROUPS

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