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1.
Thomas Meixner 《Israel Journal of Mathematics》1981,38(4):345-360
For a finite groupG letA(G) denote the group of power automorphisms, i.e. automorphisms normalizing every subgroup ofG. IfG is ap-group of class at mostp, the structure ofA (G) is shown to be rather restricted, generalizing a result of Cooper ([2]). The existence of nontrivial power automorphisms,
however, seems to impose restrictions on thep-groupG itself. It is proved that the nilpotence class of a metabelianp-group of exponentp
2 possessing a nontrival power automorphism is bounded by a function ofp. The “nicer” the automorphism—the lower the bound for the class. Therefore a “type” for power automorphisms is introduced.
Several examples ofp-groups having large power automorphism groups are given. 相似文献
2.
Narong Punnim 《Graphs and Combinatorics》2002,18(4):781-785
Let ω(G) be the clique number of a graph G. We prove that if G runs over the set of graphs with a fixed degree sequence d, then the values ω(G) completely cover a line segment [a,b] of positive integers. For an arbitrary graphic degree sequence d, we define min(ω,d) and max(ω,d) as follows:
where is the graph of realizations of d.
Thus the two invariants a:=min(ω,d) and b:=max(ω,d) naturally arise. For a graphic degree sequence d=r
n
:=(r,r,…,r) where r is the vertex degree and n is the number of vertices, the exact values of a and b are found in all situations. Since the independence number, α(G)=ω(Gˉ), we obtain parallel results for the independence number of graphs.
Received: October, 2001 Final version received: July 25, 2002
RID="*"
ID="*" Work supported by The Thailand Research Fund, under the grant number BRG/09/2545 相似文献
3.
We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra
of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators a,b,c,d. We discover a family of automorphisms for which the “twisted” Hochschild dimension coincides with the classical dimension
of
, thus avoiding the “dimension drop” in Hochschild homology seen for many quantum deformations. Strikingly, the simplest such
automorphism is the canonical modular automorphism arising from the Haar functional. In addition, we identify the twisted
cyclic cohomology classes corresponding to the three covariant differential calculi over quantum SU(2) discovered by Woronowicz. 相似文献
4.
Martin Hertweck 《Monatshefte für Mathematik》2002,242(2):1-7
Let G be a finite group whose Sylow 2-subgroups are either cyclic, dihedral, or generalized quaternion. It is shown that a class-preserving automorphism of G of order a power of 2 whose restriction to any Sylow subgroup of G equals the restriction of some inner automorphism of G is necessarily an inner automorphism. Interest in such automorphisms arose from the study of the isomorphism problem for integral group rings, see [6, 7, 13, 14]. 相似文献
5.
6.
Matthias Schwarz 《Inventiones Mathematicae》1998,133(2):353-397
A new lower bound for the number of fixed points of Hamiltonian automorphisms of closed symplectic manifolds (M,ω) is established. The new estimate extends the previously known estimates to the class of weakly monotone symplectic manifolds.
We prove for arbitrary closed symplectic manifolds with rational symplectic class that the cup-length estimate holds true
if the Hofer energy of the Hamiltonian automorphism is sufficiently small. For arbitrary energy and on weakly monotone symplectic
manifolds we define an analogon to the cup-length based on the quantum cohomology ring of (M,ω) providing a quantum cup-length estimate.
Oblatum 12-IX-1997 相似文献
7.
Martin Hertweck 《Monatshefte für Mathematik》2002,136(1):1-7
Let G be a finite group whose Sylow 2-subgroups are either cyclic, dihedral, or generalized quaternion. It is shown that a class-preserving
automorphism of G of order a power of 2 whose restriction to any Sylow subgroup of G equals the restriction of some inner automorphism of G is necessarily an inner automorphism. Interest in such automorphisms arose from the study of the isomorphism problem for
integral group rings, see [6, 7, 13, 14].
Received 30 September 2001; in revised form 10 December 2001 相似文献
8.
Ikuo Yoneda 《Archive for Mathematical Logic》2003,42(5):423-433
We show that any relational generic structure whose theory has finite closure and amalgamation over closed sets is stable
CM-trivial with weak elimination of imaginaries.
Received: 21 December 2001 /
Published online: 5 November 2002
Mathematics Subject Classification (2000): 03C45
Key words or phrases: CM-triviality – Generic structures – Stability 相似文献
9.
Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties)
polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with
the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes
for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken
into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional
case provides interesting classes of groups.
Received: 13 December 2001 / Revised version: 24 June 2002
The second author was supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107
Mathematics Subject Classification (2000): 14L27, 14M25, 19C09, 52B20 相似文献
10.
M. I. Gordin 《Journal of Mathematical Sciences》2000,99(2):1053-1060
Let T: X→X be an automorphism (a measurable invertible measure-preserving transformation) of a probability space (X, F, μ)
and let two μ-symmetric Markov generators Au and As acting on the space L2=L2 (X, F, μ) be “eigenfunctions” of the automorphism T with eigenvaluesθ
u
> 1 andθ
s
< 1, respectively. We construct an extension of the automorphism T having increasing and decreasing filtrations by means
of a transformation on the path space of these processes. Under additional conditions, we give an estimate of the maximal
correlation coefficient between the δ-fields chosen from these filtrations. Hyperbolic toral automorphisms are considered
as an example. Applications to limit theorems are given. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 61–72.
Translated by M. I. Gordin. 相似文献
11.
We consider hypercyclic composition operators on
which can be obtained from the translation operator using polynomial automorphisms of
. In particular we show that if C
S
is a hypercyclic operator for an affine automorphism S on
, then
for some polynomial automorphism Θ and vectors a and b, where I is the identity operator. Finally, we prove the hypercyclicity of “symmetric translations” on a space of symmetric analytic
functions on ℓ1.
Received: 8 June 2006 Revised: 26 September 2006 相似文献
12.
We consider the family f
a,b
(x,y)=(y,(y+a)/(x+b)) of birational maps of the plane and the parameter values (a,b) for which f
a,b
gives an automorphism of a rational surface. In particular, we find values for which f
a,b
is an automorphism of positive entropy but no invariant curve. The Main Theorem: If f
a,b
is an automorphism with an invariant curve and positive entropy, then either (1) (a,b) is real, and the restriction of f to the real points has maximal entropy, or (2) f
a,b
has a rotation (Siegel) domain.
Research supported in part by the NSF. 相似文献
13.
Daniel Lascar 《Archive for Mathematical Logic》1991,31(1):55-68
Assume that the class of partial automorphisms of the monster model of a complete theory has the amalgamation property. The beautiful automorphisms are the automorphisms of models ofT which: 1. are strong, i.e. leave the algebraic closure (inT
eq) of the empty set pointwise fixed, 2. are obtained by the Fraïsse construction using the amalgamation property that we have just mentioned. We show that all the beautiful automorphisms have the same theory (in the language ofT plus one unary function symbol for the automorphism), and we study this theory. In particular, we examine the question of the saturation of the beautiful automorphisms. We also prove that in some cases (in particular if the theory is -stable andG-trivial), almost all (in the sense of Baire categoricity) automorphisms of the saturated countable model are beautiful and conjugate. 相似文献
14.
Tullio G. Ceccherini-Silberstein 《manuscripta mathematica》2002,107(4):451-461
Let denote the free group of rank 2g. An automorphism φ? Aut(F
2
g
) is generating if N
a
φ (N
b
) = F
2
g
, where N
a
is the normal closure of and N
b
is defined analogously. We present a characterization of generating automorphisms in Aut(F
2) and observe that there exists a unique (up to equivalence) epimorphism F
2→Z×Z: this is a particular case of the Grigorchuk–Kurchanov conjecture.
This leads to further investigations for splitting homomorphisms for the pairs (F
2
g
, F
g) and (G
g, F
g) where G
g denotes the fundamental group of a closed orientable surface of genus g and a reformulation of the Poincaré and Grigorchuk–Kurchanov conjectures is derived.
Received: 1 October 2001 相似文献
15.
Liz Raquel Vivas 《Journal of Geometric Analysis》2012,22(2):352-382
We prove that there exists an automorphism of ℂ2 tangent to the identity with a domain of attraction D to the origin, biholomorphic to ℂ2, along a degenerate characteristic direction. Our automorphism of ℂ2 is conjugate to a translation in D. We also prove the existence of a curve Γ, a biholomorphic copy of ℂ, entirely contained in the boundary of D. In our construction Γ is tangent to the z-axis in a neighborhood of the origin. The automorphisms we construct also fix the w-axis; therefore we obtain D, a Fatou–Bieberbach domain that does not intersect two biholomorphic copies of ℂ locally transversal at the origin. 相似文献
16.
Antonio Kirson 《Annali dell'Universita di Ferrara》2010,56(2):327-333
An automorphism σ of a projective variety X is said to be wild if σ(Y) ≠ Y for every non-empty subvariety
Y \subsetneq X{Y \subsetneq X} . In [1] Z. Reichstein, D. Rogalski, and J.J. Zhang conjectured that if X is an irreducible projective variety admitting a wild automorphism then X is an abelian variety, and proved this conjecture for dim(X) ≤ 2. As a step toward answering this conjecture in higher dimensions we prove a structure theorem for projective varieties
of Kodaira dimension 0 admitting wild automorphisms. This essentially reduces the Kodaira dimension 0 case to a study of Calabi-Yau
varieties, which we also investigate. In support of this conjecture, we show that there are no wild automorphisms of certain
Calabi-Yau varieties. 相似文献
17.
Short proofs of normalization for the simply- typed λ-calculus,permutative conversions and Gödel's T
Inductive characterizations of the sets of terms, the subset of strongly normalizing terms and normal forms are studied in
order to reprove weak and strong normalization for the simply-typed λ-calculus and for an extension by sum types with permutative
conversions. The analogous treatment of a new system with generalized applications inspired by generalized elimination rules
in natural deduction, advocated by von Plato, shows the flexibility of the approach which does not use the strong computability/candidate
style à la Tait and Girard. It is also shown that the extension of the system with permutative conversions by η-rules is still
strongly normalizing, and likewise for an extension of the system of generalized applications by a rule of ``immediate simplification'.
By introducing an infinitely branching inductive rule the method even extends to G?del's T.
Received 12 October 1998 Published online: 19 December 2002
Mathematics Subject Classification (2000): 03B40
Keywords or phrases: λ-calculus – Permutative/commuting conversions – Sum types – Generalized application – G?del's Tq-ω-rule – Inductive characterization 相似文献
18.
R. Sh. Omanadze 《Mathematical Notes》1999,66(2):174-180
The existence of a recursively enumerable (RE)T-degreea that does not contain an RE semirecursive setA ∈a with theQ-universal splitting property is proved. Each nonrecursive RE contiguous degree contains an RE setA with the universalT-Q-reduction property, butA is notT-Q-maximal. Each nonrecursive REW-degree contains an RE setA with the universalW-sQ-reduction property, butA is notW-sQ-maximal. Each creative set is partially semimaximal.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 220–230, August, 1999. 相似文献
19.
Ram U. Verma 《Positivity》2009,13(4):771-782
First, based on η-maximal accretiveness, a generalization to Rockafellar’s theorem (1976) in the context of approximating a solution to a general
inclusion problem involving a multivalued η-maximal accretive mapping using the proximal point algorithm in a q-uniformly smooth Banach space setting is considered.
Then an application to a minimization problem of a functional is examined. The general framework for η-maximal accretiveness generalizes the general theory of multivalued maximal monotone mappings.
相似文献
20.
Marat M. Arslanov Iskander Sh. Kalimullin Andrea Sorbi 《Archive for Mathematical Logic》2001,40(8):597-614
We show that the Δ0
2 enumeration degrees are dense. We also show that for every nonzero n-c. e. e-degree a, with n≥ 3, one can always find a nonzero 3-c. e. e-degree b such that b < a on the other hand there is a nonzero ωc. e. e-degree which bounds no nonzero n-c. e. e-degree.
Received: 13 June 2000 / Published online: 3 October 2001 相似文献