Let U be a maximal unipotent subgroup of a finite classical group in good characteristic. We prove the existence of a bijection between U and the associated Lie algebra preserving centralizers. As a consequence, we obtain information on the sizes of the conjugacy classes of U. Similar results are proved in the exceptional cases.
Previtali, A. (1999). Maps behaving like exponentials and maximal unipotent subgroups of groups of Lie type. COMMUNICATIONS IN ALGEBRA, 27(5), 2511-2519 [10.1080/00927879908826577].
Maps behaving like exponentials and maximal unipotent subgroups of groups of Lie type
PREVITALI, ANDREA
1999
Abstract
Let U be a maximal unipotent subgroup of a finite classical group in good characteristic. We prove the existence of a bijection between U and the associated Lie algebra preserving centralizers. As a consequence, we obtain information on the sizes of the conjugacy classes of U. Similar results are proved in the exceptional cases.
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