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1.
V. M. Tsvetkov 《Journal of Mathematical Sciences》1984,24(4):480-482
Examples are given of fields of algebraic numbers for which the Galois group of a maximal -extension with ramification at the divisors ofl is a Demushkin group.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 103, pp. 146–149, 1980. 相似文献
2.
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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Jack Sonn 《Israel Journal of Mathematics》1979,34(1-2):97-105
LetF be a global field,n a positive integer not divisible by the characteristic ofF. Then there exists a finite extensionE ofF whose class group has a cyclic direct summand of ordern. This theorem, in a slightly stronger form, is applied to determine completely, on the basis of the work of Fein and Schacher,
the structure of the Brauer group Br(F()) of the rational function fieldF(t). As a consequence of this, an additional theorem of the above authors, together with a note at the end of the paper, imply
that Br(F(t)) ≊ Br(F(t
1, ···,t
n)), wheret
1, ···,t
n are algebraically independent overF. 相似文献
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In this article, we establish that every finite abelian group is isomorphic to the autocommutator subgroup of some finite
abelian group.
Received: 21 September 2007 相似文献
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F. Rotmaer 《Ukrainian Mathematical Journal》1977,29(2):162-167
10.
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
11.
Ben Fairbairn 《Monatshefte für Mathematik》2016,181(4):761-777
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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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We study groups whose structure is similar to the structure of metacyclic groups. These groups play an important role in the investigation of groups with normal subgroups. 相似文献
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Groups are classified whose automorphism group is minimal non-nilpotent.The first author wishes to thank the Mathematics Department of Napoli for its warm hospitality for the time of writing this paper. 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