The sylow 2-subgroups of the finite classical groups
نویسندگان
چکیده
منابع مشابه
Ranks of the Sylow 2-Subgroups of the Classical Groups
Let S be a 2-group. The rank (normal rank) of S is the maximal dimension of an elementary abelian subgroup (a normal elementary abelian subgroup) of S over Z2. The purpose of this article is to determine the rank and normal rank of S, where S is a Sylow 2-subgroup of the classical groups of odd characteristic.
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A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core of $H$ in $G$. We characterize the supersolubility of finite groups $G$ with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.
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0. Introduction A 2-group is called realisable if it is isomorphic to a Sylow 2-subgroup of a finite simple group. It is well known that very few 2-groups are realisable (see [HL], [M]). In order to understand such realisable 2-groups, one would like to find a set of invariance of 2-groups which enables us to differentiate Ω1 (the set of realisable 2-groups) from Ω2 (the set of non-realisable 2...
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In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...
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The aim of this paper is to give a direct approach to the study of the Sylow ^-subgroups Sn of the symmetric group of degree pn. [We assume throughout that p^2.] Many of the results are already known and are treated in a paper by Kaloujnine where he uses a particular representation by means of "reduced polynomials."1 It has seemed worth while to restate some of his results using the concept of ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1964
ISSN: 0021-8693
DOI: 10.1016/0021-8693(64)90030-4