# Some rings of invariants that are Gorenstein

Tamir Buqaie – GJM, Volume 8, Issue 1 (2023), 78-82.

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- octobre 26, 2023
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Let G be a finite subgroup of SL(V) and let V be a 3-dimensional vector space over a finite field \mathbb F of positive characteristic p which divides |G|. We denote by S(V) the symmetric algebra and by S(V)^{G} the subring of G-invariants. Let T(G) be the transvections group. In this paper we classify the Gorenstein rings of the form S(V)^{G}, where V is a decomposable G-module of the form V=\mathbb F v\oplus W, with \mathbb Fv and W being G-submodules with \dim_\mathbb F W=2. There are several cases for T(G) and W, and so for each of them, we provide a sufficient and necessary condition for G as above to ensure the Gorenstein property of S(V)^G.

**Categories:**Issue1

#### Milestones:

Received: September 22, 2022

Accepted: August 1, 2023

Revised: September 16, 2023

Published online: October 22, 2023

#### Authors:

__Tamir Buqaie__

Department of Mathematics,

Faculty of Natural Sciences, University of Haifa,

Mount Carmel, Haifa 31905, Israel.