Extraction of Small Rank Unipotent Elements in GL(4, K)

Let K be a field with at least 19 elements. It is proved that any subgroup of 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 f...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-06, Vol.264 (1), p.86-95
Main Author: Nesterov, V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Subgroups
Toruses
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Summary:Let K be a field with at least 19 elements. It is proved that any subgroup of 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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05982-x