منابع مشابه
On Integral Groups . Ill : Normalizers
Methods for determining a generating set for the normalizer of a finite group of n X n integral matrices, i.e., an «-dimensional crystallographic point group, are discussed. Necessary and sufficient conditions for the finiteness of such a normalizer are derived, and several examples of the application of the methods to cases when the normalizer is infinite are presented. This is the third in a ...
متن کاملNormalizers in Limit Groups
Let Γ be a limit group, S ⊂ Γ a subgroup, and N the normaliser of S. If H1(S,Q) has finite Q-dimension, then S is finitely generated and either N/S is finite or N is abelian. This result has applications to the study of subdirect products of limit groups. Limit groups (or ω-residually free groups) have received a good deal of attention in recent years, primarily due to the groundbreaking work o...
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The general problem of computing the normalizer, in a finite permutat ion group G, of a subgroup H has long been recognized as being unusually difficult to solve efficiently. The corresponding problem for centralizers is much easier, although this too has some bad cases. The solution to the centralizer problem is relatively simple and probably difficult to improve upon, whereas there seems to b...
متن کاملNormalizers of Parabolic Subgroups of Coxeter Groups
We improve a bound of Borcherds on the virtual cohomological dimension of the non-reflection part of the normalizer of a parabolic subgroup of a Coxeter group. Our bound is in terms of the types of the components of the corresponding Coxeter subdiagram rather than the number of nodes. A consequence is an extension of Brink’s result that the non-reflection part of a reflection centralizer is fre...
متن کاملIntegral Control on Lie Groups
In this paper, we extend the popular integral control technique to systems evolving on Lie groups. More explicitly, we provide an alternative definition of “integral action” for proportional(derivative)-controlled systems whose configuration evolves on a nonlinear space, where configuration errors cannot be simply added up to compute a definite integral. We then prove that the proposed integral...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1973
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1973-0333025-7