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Subgroups containing a torus and related to the quotient field of a factorial ring. (Russian) Zbl 1081.20055
Let $$R$$ be a factorial integral ring with identity and let $$k$$ be the quotient field of $$R$$. Let $$d$$ be a square-free element of $$R$$ and let $$K$$ be a splitting field of $$x^n-d$$. It is well known that $$K^*$$ can be isomorphically embedded into $$\operatorname{Aut}_k(K)\simeq\text{GL}_n(k)$$. The authors call the image $$T(d)$$ of $$K^*$$ in $$\text{GL}_n(k)$$ a nonsplit maximal torus. They describe subgroups of $$\text{GL}_n(k)$$ maximal among those containing $$T(d)$$ and not contained in $$\text{SL}_n(k)$$.
##### MSC:
 20G15 Linear algebraic groups over arbitrary fields 20E15 Chains and lattices of subgroups, subnormal subgroups 20E07 Subgroup theorems; subgroup growth
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