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JOURNALS // Fundamentalnaya i Prikladnaya Matematika // Archive

Fundam. Prikl. Mat., 2024 Volume 25, Issue 1, Pages 205–212 (Mi fpm1966)

Universal-existential equivalence of linear groups

P. Pritup

Lomonosov Moscow State University

Abstract: In this paper, we prove that the groups $\mathrm{GL}$ and $\mathrm{SL}$ over infinite fields of characteristics not equal to $2$ are $(\forall \exists)$-equivalent if and only if their dimensions coincide and the corresponding fields are $(\forall \exists)$-equivalent.

UDC: 510.67+512.54.0+512.743



© Steklov Math. Inst. of RAS, 2024