共查询到20条相似文献,搜索用时 15 毫秒
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Gary Kennedy 《代数通讯》2013,41(9):2821-2839
Sacerdote [Sa] has shown that the non-Abelian free groups satisfy precisely the same universal-existential sentences Th(F2)??? in a first-order language Lo appropriate for group theory. It is shown that in every model of Th(F2)??? the maximal Abelian subgroups are elementarily equivalent to locally cyclic groups (necessarily nontrivial and torsion free). Two classes of groups are interpolated between the non-Abelian locally free groups and Remeslennikov’s ?-free groups. These classes are the almost locally free groups and the quasi-locally free groups. In particular, the almost locally free groups are the models of Th(F2)??? while the quasi-locally free groups are the ?-free groups with maximal Abelian subgroups elementarily equivalent to locally cyclic groups (necessarily nontrivial and torsion free). Two principal open questions at opposite ends of a spectrum are: (1.) Is every finitely generated almost locally free group free? (2.) Is every quasi-locally free group almost locally free? Examples abound of finitely generated quasi-locally free groups containing nontrivial torsion in their Abelianizations. The question of whether or not almost locally free groups have torsion free Abelianization is related to a bound in a free group on the number of factors needed to express certain elements of the derived group as a product of commutators 相似文献
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A. Kontogeorgis 《Mathematische Zeitschrift》2008,259(3):471-479
For nonsingular projective curves defined over algebraically closed fields of positive characteristic the dependence of the
ramification filtration of decomposition groups of the automorphism group with Weierstrass semigroups attached at wild ramification
points is studied. A faithful representation of the p-part of the decomposition group at each wild ramified point to a Riemann–Roch space is defined. 相似文献
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We prove that for smooth projective threefolds whose anticanonical divisors are nef, the second Chern classes are pseudo-effective under a weak assumption. As an application, the pseudo-effectivity of the second Chern classes implies that Kawamatas Effective Non-vanishing Conjecture holds for such threefolds.Mathematics Subject Classification (2000): Primary 14C17, Secondary 14J30 相似文献
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M. Hashemi 《Ukrainian Mathematical Journal》2009,61(12):1995-2007
We study two classes of 2-generated nilpotent groups of nilpotency class 2 and compute the order of their automorphism groups. 相似文献
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Vladimir Tolstykh 《Journal of Pure and Applied Algebra》2011,215(9):2086-2098
Let F be an infinitely generated free group and let R be a fully invariant subgroup of F such that (a) R is contained in the commutator subgroup F′ of F and (b) the quotient group F/R is residually torsion-free nilpotent. Then the automorphism group of the group F/R′ is complete. In particular, the automorphism group of any infinitely generated free solvable group of derived length at least two is complete.This extends a result by Dyer and Formanek (1977) [7] on finitely generated groups Fn/R′ where Fn is a free group of finite rank n at least two and R a characteristic subgroup of Fn. 相似文献
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In one of our recent papers, the associative and the Lie algebras of Weyl typeA[D]=A⊗F[D] were defined and studied, whereA is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebraD ofA. In the present paper, a class of the above associative and Lie algebrasA[D] with F being a field of characteristic 0,D consisting of locally finite but not locally nilpotent derivations ofA, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined 相似文献
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Hisao Yoshihara 《Journal of Algebra》2009,321(5):1463-1472
Let G be the Galois group of a Galois point for a plane curve C. An element of G induces a birational transformation of C. We study if it can be extended to a projective or birational transformation of the plane. In the course of the study we give the defining equation of a rational curve with the Galois point. Furthermore, we introduce a special birational transformation in order to make the defining equation into a simpler form. 相似文献
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In this paper we give an effective criterion as to when a positive integer q is the order of an automorphism of a smooth hypersurface of dimension n and degree d, for every d ≥ 3, n ≥ 2, (n, d) ≠ (2, 4), and gcd(q, d) = gcd(q, d ? 1) = 1. This allows us to give a complete criterion in the case where q = p is a prime number. In particular, we show the following result: If X is a smooth hypersurface of dimension n and degree d admitting an automorphism of prime order p then p < (d ? 1) n+1; and if p > (d ? 1) n then X is isomorphic to the Klein hypersurface, n = 2 or n + 2 is prime, and p = Φ n+2(1 ? d) where Φ n+2 is the (n+2)-th cyclotomic polynomial. Finally, we provide some applications to intermediate jacobians of Klein hypersurfaces. 相似文献
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Akitaka Kishimoto Alex Kumjian 《Transactions of the American Mathematical Society》1998,350(10):4127-4148
Let be a simple unital algebra of real rank zero. It is shown below that the range of the natural map from the approximately inner automorphism group to coincides with the kernel of the map .
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We describe the asymptotic behavior of automorphisms of totally disconnected locally compact groups in terms of a set of `directions'
which comes equipped with a natural pseudo-metric. The structure at infinity obtained by completing the induced metric quotient
space of the set of directions recovers familiar objects such as: the set of ends of the tree for the group of inner automorphisms
of the group of isometries of a regular locally finite tree; and the spherical Bruhat-Tits building for the group of inner
automorphisms of the set of rational points of a semisimple group over a local field.
Research supported by A.R.C. Grant DP0208137. 相似文献
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One proves that any rank 3 topological vector bundle on a homogeneous rational 3-fold has an algebraic structure. The proof uses extensions of ideals by rank 2 vector bundles. The paper also contains a construction of rank 3 vector bundles on 3-folds using extensions of ideals by rank 2 reflexive sheaves. 相似文献