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Extraction of small rank unipotent elements in \(\operatorname{GL}(4, K)\). (English. Russian original) Zbl 07553415

J. Math. Sci., New York 264, No. 1, 86-95 (2022); translation from Zap. Nauchn. Semin. POMI 492, 134-148 (2020).
Summary: Let \(K\) be a field with at least 19 elements. It is proved that any subgroup of \(\operatorname{GL}(4, K)\) generated by a pair of 2-tori contains unipotent elements of rank 1 or 2. Taking into account previous papers of N. A. Vavilov and the author, this result is valid for any general linear group. It is one of the first steps in studying subgroups generated by a pair of microweight tori in Chevalley groups.

MSC:

20Gxx Linear algebraic groups and related topics
11Txx Finite fields and commutative rings (number-theoretic aspects)
20Hxx Other groups of matrices
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