A note concerning fixed points of parabolic subgroups of unitary reflection groups
نویسندگان
چکیده
منابع مشابه
a note on fixed points of automorphisms of infinite groups
motivated by a celebrated theorem of schur, we show that if~$gamma$ is a normal subgroup of the full automorphism group $aut(g)$ of a group $g$ such that $inn(g)$ is contained in $gamma$ and $aut(g)/gamma$ has no uncountable abelian subgroups of prime exponent, then $[g,gamma]$ is finite, provided that the subgroup consisting of all elements of $g$ fixed by $gamma$ has finite index. so...
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Introduction. Any finite group of linear transformations on n variables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of unitary transformations (5, p. 257). Such a group may be thought of as a group of congruent transformations, keeping the origin fixed, in a unitary space Un of n dimensions, in which the p...
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A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion...
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We use geometry of Davis complex of a Coxeter group to investigate finite index reflection subgroups of Coxeter groups. The main result is the following: if G is an infinite indecomposable Coxeter group and H ⊂ G is a finite index reflection subgroup then the rank of H is not less than the rank of G. This generalizes results of [7]. We also describe some properties of the nerves of the group an...
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The maximality of certain symplectic subgroups of unitary groups PSUn(K), n ≥ 4, (K any field admitting a non–trivial involutory automorphism) belonging to the class C5 of Aschbacher is proved. Furthermore some related geometry in the case n = 4 and K finite is investigated. Mathematics Subject Classification (2002): 20G40, 20G28
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 1999
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(00)87908-2