Alternating groups as maximal subgroups of the special orthogonal groups over the field of two elements
نویسندگان
چکیده
منابع مشابه
Triple factorization of non-abelian groups by two maximal subgroups
The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...
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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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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1981
ISSN: 0021-8693
DOI: 10.1016/0021-8693(81)90186-1