Maximal subgroups of finite symplectic groups stabilizing spreads of lines
نویسندگان
چکیده
منابع مشابه
Maximal Subgroups of Finite Orthogonal Groups Stabilizing Spreads of Lines
It is well known to devotees of the simple groups or of the classical groups that the special unitary group SUn(q ) is a subgroup of the commutator subgroup Q2n{q) of one of the orthogonal groups O2n{q). The geometry behind this containment is easy to describe (see Section 2). Regarding the field L = GF(q) as a vector space over K = GF(<jf) we obtain a bijection x -* x between the vector spaces...
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We prove that, for q odd and n ≥ 3, the group G = On(q) · 2 is maximal in either the orthogonal group O2n(q) or the special orthogonal group SO2n(q). The group G corresponds to the stabilizer of a spread of lines of PG(2n − 1, q) in which some lines lie on a quadric, some are secant to the quadric and others are external to the quadric.
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What ingredients are necessary to describe all maximal subgroups of the general finite group G? This paper is concerned with providing such an analysis. A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal subgroup N of G correspond, under the natural projection, to the maximal subgroups of the quotient...
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متن کاملOn Maximal Subgroups of Finite Classical Groups
In 1] M. Aschbacher described the structure of the possible maximal subgroups of a classical group G with natural module M. Each such subgroup is either a member of a canonical class of subgroups, or it is the normalizer of a quasi-simple, absolutely irreducible subgroup H of G. In the latter case suppose that H is a classical group whose deening characteristic is coprime to that of G. The aim ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00639-7