Small rank permutation representations of finite Chevalley groups
نویسندگان
چکیده
منابع مشابه
Small degree representations of finite Chevalley groups in defining characteristic
We determine for all simple simply connected reductive linear algebraic groups defined over a finite field all irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l our bound is proportional to l3 and for rank 11 m...
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In 1832, Galois [ll, pp. 41 l-4121 determined the smallest degree of a faithful permutation representation of PSL(2, 4) for q a prime; the case q a prime power was handled much later, reportedly first in unpublished work of Moore in 1894 (see Loewy [22]). Th e corresponding problem was solved for Sp(4, q), q an odd prime or prime power, by Dickson [9] and Mitchell [27], respectively; and for SL...
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We prove a version of the O'Nan-Scott Theorem for detinably primitive permutation groups of finite Morley rank. This yields questions about structures of finite Morley rank of the form (F, + , . , / / ) where (F, +,.) is an algebraically closed field and H is a central extension of a simple group with /Y=sGL(rt, F). We obtain partial results on such groups H, and show for example that if char(/...
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Introduction Groups of finite Morley rank made their first appearance in model theory as binding groups, which are the key ingredient in Zilber's ladder theorem and in Poizat's explanation of the Picard-Vessiot theory. These are not just groups, but in fact permutation groups acting on important definable sets. When they are finite, they are connected with the model theoretic notion of algebrai...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1974
ISSN: 0021-8693
DOI: 10.1016/0021-8693(74)90057-x