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Nonlinearity of the Automorphism Groups of Some Free Algebras 总被引:2,自引:2,他引:0
We prove that the groups of tame automorphisms of a free Lie algebra (free associative algebra, absolutely free algebra, algebra of polynomials) of rank at least four over a field of characteristic zero admit no faithful representation by matrices over any field. 相似文献
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A group G is said to have the Bergman property (the propertyof uniformity of finite width) if given any generating X withX = X1 of G, we have that G = Xk for some natural k,that is, every element of G is a product of at most k elementsof X. We prove that the automorphism group Aut(N) of any infinitelygenerated free nilpotent group N has the Bergman property. Also,we obtain a partial answer to a question posed by Bergman byestablishing that the automorphism group of a free group ofcountably infinite rank is a group of uniformly finite width. 相似文献
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Communicated by 相似文献
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Clarification is suggested for the early notion of homomorphisms of fuzzy groups. Conditions are considered for fulfilment of various properties of homomorphisms of ordinary groups as well as properties specific to systems with a fuzzy operation. Correctness is discussed of the introduced notion of preservation of a fuzzy operation. 相似文献
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Clarification is suggested for the early notion of homomorphisms of fuzzy groups. Conditions are considered for fulfilment of various properties of homomorphisms of ordinary groups as well as properties specific to systems with a fuzzy operation. Correctness is discussed of the introduced notion of preservation of a fuzzy operation. 相似文献
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A proof is given of the following theorem, which characterizesfull automorphism groups of ordered abelian groups: a groupH is the automorphism group of some ordered abelian group ifand only if H is right-orderable. 2000 Mathematics Subject Classification20K15, 20K20, 20F60, 20K30 (primary); 03E05 (secondary). 相似文献
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It is a well-known fact that characters of a finite group can give
important information about the structure of the group. It was also
proved by the third author that a finite simple group can be
uniquely determined by its character table. Here the authors attempt
to investigate how to characterize a finite almost-simple group by
using less information of its character table, and successfully
characterize the automorphism groups of Mathieu groups by their
orders and at most two irreducible character degrees of their
character tables. 相似文献
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We study properties of continuous homomorphisms
from β S into T* and
from S* into T*, where S denotes a countably
infinite semigroup and T denotes a countably infinite
group. We show that they have striking algebraic properties
if they do not arise as continuous
extensions of homomorphisms from S to T. 相似文献
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Abstract Homomorphisms of Algebraic Groups 总被引:2,自引:0,他引:2
In this paper we are concerned with abstract homomorphisms fromone algebraic group to another. That is, group homomorphismswhere there is no assumption of rationality. Let K be an infiniteperfect field and L an algebraically closed field of the samecharacteristic. Throughout G(K) will denote a Chevalley groupof universal type over K. 相似文献
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Droste Manfred; Giraudet Michele; Gobel Rudiger 《Journal London Mathematical Society》2001,64(3):565-575
It is shown that each group is the outer automorphism groupof a simple group. Surprisingly, the proof is mainly based onthe theory of ordered or relational structures and their symmetrygroups. By a recent result of Droste and Shelah, any group isthe outer automorphism group Out (Aut T) of the automorphismgroup Aut T of a doubly homogeneous chain (T, ). However, AutT is never simple. Following recent investigations on automorphismgroups of circles, it is possible to turn (T, ) into a circleC such that Out (Aut T) Out (Aut C). The unavoidable normalsubgroups in Aut T evaporate in Aut C, which is now simple,and the result follows. 相似文献
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Brent Kerby 《代数通讯》2013,41(12):5087-5103
In 1993, Muzychuk [23] showed that the rational Schur rings over a cyclic group Z n are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Z n . This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G in a natural way. Our main result is that any finite group may be represented as the (algebraic) automorphism group of such a rational Schur ring over an abelian p-group, for any odd prime p. In contrast, over a cyclic group the automorphism group of any Schur ring is abelian. We also prove a converse to the well-known result of Muzychuk [24] that two Schur rings over a cyclic group are isomorphic if and only if they coincide; namely, we show that over a group which is not cyclic, there always exist distinct isomorphic Schur rings. 相似文献
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Mathematical Notes - 相似文献
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Philipp Lücke 《代数通讯》2013,41(10):3625-3630
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If G is a finite group and if A is a group of automorphisms of G whose fixed point subgroup is C
G
(A) then every subgroup F of C
G
(A) acts on the set of orbits of A in G. The peculiarities of this action are used here to derive several results on the number of orbits of A in an economical manner.Original Russian Text Copyright © 2005 Deaconescu M. and Walls G. L.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 533–537, May–June, 2005. 相似文献
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James D. Lewis 《Mathematische Nachrichten》1993,160(1):205-221
Let X be a projective algebraic manifold of dimension n (over C), CH1(X) the Chow group of algebraic cycles of codimension l on X, modulo rational equivalence, and A1(X) ? CH1(X) the subgroup of cycles algebraically equivalent to zero. We say that A1(X) is finite dimensional if there exists a (possibly reducible) smooth curve T and a cycle z∈CH1(Γ × X) such that z*:A1(Γ)-A1(X) is surjective. There is the well known Abel-Jacobi map λ1:A1(X)-J(X), where J(X) is the lth Lieberman Jacobian. It is easy to show that A1(X)→J(X) A1(X) finite dimensional. Now set with corresponding map A*(X)→J(X). Also define Level . In a recent book by the author, there was stated the following conjecture: where it was also shown that (?) in (**) is a consequence of the General Hodge Conjecture (GHC). In this present paper, we prove A*(X) finite dimensional ?? Level (H*(X)) ≤ 1 for a special (albeit significant) class of smooth hypersurfaces. We make use of the family of k-planes on X, where ([…] = greatest integer function) and d = deg X; moreover the essential technical ingredients are the Lefschetz theorems for cohomology and an analogue for Chow groups of hypersurfaces. These ingredients in turn imply very special cases of the GHC for our choice of hypersurfaces X. Some applications to the Griffiths group, vanishing results, and (universal) algebraic representatives for certain Chow groups are given. 相似文献
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The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring, self-vanishing of Ext and Tor for a finitely generated module admitting such an irreducible homomorphism forces the ring to be regular. 相似文献
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在这篇注记中,我们利用群的射影极限性质证明了广义四元数群的Coleman外自同构群或者是1或者是一个初等阿贝尔2-群. 相似文献
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We extend the Dikranjan-Uspenskij notions of c-compact and h-complete topological group to the morphism level, study the stability properties of the newly defined types of maps, such as closure under direct products, and compare them with their counterparts in topology. We assume Hausdorffness only when our proofs require us to do so, which leads to new results and the affirmation of some facts that were known in a Hausdorff context. 相似文献