Conjugacy classes of centralizers in unitary groups
نویسندگان
چکیده
منابع مشابه
Conjugacy Classes of Centralizers in G 2
Let G be an algebraic group of type G2 over a field k of characteristic 6= 2, 3. In this paper we calculate centralizers of semisimple elements in anisotropic G2. Using these, we show explicitly that there are six conjugacy classes of centralizers in the compact real form of G2. AMS Subject Classification: 20G20, 17A75.
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Of course, in that problem we have to take into account that the class sizes impose restrictions on the group structure. E.g. if the sizes are {1, p}, then the nilpotency class has to be 2. More precisely: the class sizes of a p-group G are {1, p} iff |G′| = p (Knoche; see also Theorem 3 below). But we can ask, e.g., if, given any set S ≠ {1, p} of p-powers, does there exist a group of class 3 ...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2018
ISSN: 1435-4446,1433-5883
DOI: 10.1515/jgth-2018-0036