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We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from
a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the
algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic
groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain
an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences
of K(Γ,1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory. 相似文献
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We construct a full class of nilpotent groups of class 2 of an arbitrary infinite
cardinality . Their centers, commutator subgroups and factors modulo the center will be the
same and a homogeneous direct sum of a group of rank 1 or 2. Their automorphism groups will
coincide and the factor group modulo the stabilizer could be an arbitrary group of size $\leqq$ . 相似文献
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F. Rotmaer 《Ukrainian Mathematical Journal》1977,29(2):162-167
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This work was supported by the DFG and by a Polish grant BW/5100-5-0116-3. 相似文献
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Annals of Global Analysis and Geometry - We compute the full isometry group of any left-invariant metric on a simply connected, non-unimodular Lie group of dimension three. As an application, we... 相似文献
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D. G. Khramtsov 《Algebra and Logic》2005,44(2):117-131
It is proved that any non-trivial endomorphism of an automorphism group AutFn of a free group Fn, for n 3, either is an automorphism or factorization over a proper automorphism subgroup. An endomorphism of AutF2 is an automorphism, or else a homomorphism onto one of the groups S3, D8, Z2 × Z2, Z2, or
(Z2 × Z2). A non-trivial homomorphism of AutFn into AutFm, for n 3, m 2, and n > m, is a homomorphism onto Z2 with kernel SAutFn. As a consequence, we obtain that AutFn is co-Hopfian.Supported by RFBR grant No. 02-01-00293 and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 211–237, March–April, 2005. 相似文献
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We establish the validity of the inclusion G/N∈
X for groups G ∈
X under certain restrictions on N ⊴ G, where X is one of the following classes, the class of locally graded groups, the class of RI-groups, or the class for a fixed group variety .
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1545–1553, November, 1998. 相似文献
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D. G. Khramtsov 《Mathematical Notes》1985,38(3):721-724
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Manfred Kolster 《Mathematische Annalen》1979,241(2):129-158
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Published in Algebra i Logika, Vol. 29, No. 6, pp. 746–751, November–December, 1990. 相似文献
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Andrzej Szczepański 《manuscripta mathematica》1996,90(1):383-389
Let Γ be a Bieberbach group—that is a torsion free crystallographic group. In this paper we give a list of the isomorphism
types of all holonomy groups of five-dimensional Bieberbach groups. An application to the problem of estimating the covolume
of a discrete group of orientation-preserving isometries of hyperbolic 6-space is also given.
This work was supported by Polish grant nr.0627/P3/93/04 相似文献