Combinatorial and logical aspects of linear groups and Chevalley groups

E. I. Bunina; A. V. Mikhalev

doi:10.1007/s10440-004-5586-4

Combinatorial and logical aspects of linear groups and Chevalley groups

E. I. Bunina
, A. V. Mikhalev

Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The combinatorial and logical aspects of linear and Chevalley groups were studied. The elementary properties of linear groups were posed for the groups GL_n(K), SL_n(K), PGL_n(K) and PSL_n(K). The Mal'cev theorem on elementary equivalence of linear groups over fields was generalized to the case of linear groups over rings and skewfields. The structural theorem proved that the groups G(m, K₁) and G(n, K ₂ are elementary equivalent if and only if m=n and the fields K ₁ and K₂ are elementary equivalent.

Original language	English
Pages (from-to)	57-74
Number of pages	18
Journal	Acta Applicandae Mathematicae
Volume	85
Issue number	1-3
DOIs	https://doi.org/10.1007/s10440-004-5586-4
State	Published - Jan 2005
Externally published	Yes

Keywords

Chevalley groups
Elementary equivalence
Linear groups

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10.1007/s10440-004-5586-4

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AB - The combinatorial and logical aspects of linear and Chevalley groups were studied. The elementary properties of linear groups were posed for the groups GLn(K), SLn(K), PGLn(K) and PSLn(K). The Mal'cev theorem on elementary equivalence of linear groups over fields was generalized to the case of linear groups over rings and skewfields. The structural theorem proved that the groups G(m, K1) and G(n, K 2 are elementary equivalent if and only if m=n and the fields K 1 and K2 are elementary equivalent.

KW - Chevalley groups

KW - Elementary equivalence

KW - Linear groups

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Combinatorial and logical aspects of linear groups and Chevalley groups

Abstract

Keywords

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