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LetO2\mathcal{O}_{2}andO2′\mathcal{O}^{\prime}_{2}be two distinct finite local rings of length two with residue field of characteristic . LetG⁢(O2)\mathbb{G}(\mathcal{O}_{2})andG⁢(O2′)\mathbb{G}(\mathcal{O}^{\prime}_{2})be the groups of points of any reductive group scheme  over ℤ such that  is very good forG×Fq\mathbb{G}\times\mathbb{F}_{q}orG=GLn\mathbb{G}=\operatorname{GL}_{n}. We prove that there exists an isomorphism of group algebrasK⁢G⁢(O2)≅K⁢G⁢(O2′)K\mathbb{G}(\mathcal{O}_{2})\cong K\mathbb{G}(\mathcal{O}^{\prime}_{2}), where  is a sufficiently large field of characteristic different from .

The ℓ-modular representation of reductive groups over finite local rings of length two