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- W2326184158 abstract " Everything remains to be done concerning the automorphisms of unitary groups over infinite fields (or reflexive sfields) of characteristic 2; Thus wrote Dieudonne in 1951 in his book On the automorphismns of the classical groups [4]. Again in 1963 in his book La geomretrie des groupes classiques [6] (see page 100), he remarks that this problem as yet is still unsolved. In 1967, Speigel [10, 11] answered this question provided the Witt index is greater than 1 and the dimension of the underlying space is greater than 5. Essentially, these assumptions insure the existence of enough involutions and the arguments depend heavily upon this existence. is exactly the trouble when the Witt index is 1 or 0, i. e. there are very few involutions. Indeed, when the space is anisotropic, there are no involutions except lv. O'Meara in 1968 [7], was faced with the same difficulty. In this work, he states This is a more serious matter since all known approaches to the automorphism question either make repeated and essential use of such transformations, or else are based on results of Lie algebras which give the automorphisms only over finite fields and, with some difficulty, over algebraically closed 2 As was O'Meara, we are forced to find a new method if we are to solve this problem and this is precisely the purpose of this paper, i. e. to introduce a new method and with this method determine the automorphims of the unitary groups over fields. The precise result which we prove is the following: Let V be any regular n-ary hermitian space over an infinite field of characteristic 2. Suppose n ? 3 and the Witt index is 1 or 0. Let A be either 9A (V) or %i,+ (V) and A an arbitrary automorphism of A. Then A has the form A (u) =X (a'gucg-" @default.
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- W2326184158 date "1971-04-01" @default.
- W2326184158 modified "2023-09-24" @default.
- W2326184158 title "The Automorphisms of Unitary Groups Over a Field of Characteristic 2" @default.
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- W2326184158 doi "https://doi.org/10.2307/2373382" @default.
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