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1.
IfG is a finite solvable group andH is a maximal nilpotent subgroup ofG containingF(G), we show that there is a canonical basisP(G|H) of the space of class functions onG vanishing off anyG-conjugate ofH which consists of characters. ViaP(G|H) it is possible to partition the irreducible characters ofG into “blocks”. These behave like Brauerp-blocks and a Fong theory for them can be developed.
Research partially supported by DGICYT and MEC. 相似文献
2.
Primes dividing the degrees of the real characters 总被引:1,自引:0,他引:1
Let G be a finite group and let Irr(G) denote the set of all complex irreducible characters of G. The Ito–Michler Theorem asserts that if a prime p does not divide the degree of any χ Irr(G) then a Sylow p-subgroup P of G is normal in G. We prove a real-valued version of this theorem, where instead of Irr(G) we only consider the subset Irrrv(G) consisting of all real-valued irreducible characters of G. We also prove that the character degree graph associated to Irrrv(G) has at most 3 connected components. Similar results for the set of real conjugacy classes of G have also been obtained.
Part of this paper was done while the second author visited the Mathematics Department of the Università di Firenze. He would
like to thank the Department for its hospitality. The authors are also grateful to F. Lübeck for helping them with some computer
calculations.
The research of the first author was partially supported by MIUR research program “Teoria dei gruppi ed applicazioni”. This
research of the second author was partially supported by the Spanish Ministerio de Educación y Ciencia proyecto MTM2004-06067-C02-01.
The third author gratefully acknowledges the support of the NSA and the NSF. 相似文献
3.
R. I. Grigorchuk 《Mathematical Notes》1996,60(3):274-282
The paper is devoted to the study of weights on groups. A connection between weight functions and harmonic functions is established.
A relationship between the weight theory on groups with the “Tychonoff property” and the theory of bounded cohomology is presented.
It is proved that the Beurling algebraℓ1 (G, ω) constructed for the weightω is amenable if and only if the groupG is amenable and the weightω is equivalent to a multiplicative characterχ:G→ℝ+.
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 448–460, September, 1996.
This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-00974 and by the
INTAS Foundation under grant No. 94-3420. 相似文献
4.
LetW be a real algebraic set. We show that the following families of integer-valued functions onW coincide: (i) the functions of the formω →λ(X
ω
), where X
ω
are the fibres of a regular morphismf :X →W of real algebraic sets, (ii) the functions of the formω →χ(X
ω
), where X
ω
are the fibres of a proper regular morphismf :X →W of real algebraic sets, (iii) the finite sums of signs of polynomials onW. Such functions are called algebraically constructible onW. Using their characterization in terms of signs of polynomials we present new proofs of their basic functorial properties
with respect to the link operator and specialization.
Research partially supported by an Australian Research Council Small Grant. Second author also partially supported by KBN
610/P3/94. 相似文献
5.
Fred B. Weissler 《Israel Journal of Mathematics》1978,29(2-3):265-275
Under certain circumstances, the Trotter-Lie formulaW
t=lim(U
t/nVt/n)
n
is used to construct a non-linear semi-groupW
t on closed subsets ofL
P, 1≦p<∞. In particular we consider the situation whereU
t=e
tA is a positivity preservingC
0 (linear) semi-group andV
t is generated by a (non-linear) functionF with certain monotonicity properties. In general,A andF are “singular” onL
p and no requirement is made that one of them be “relatively bounded” with respect to the other. The generator of the resulting
semi-groupW
t turns out to be an extension ofA +F restricted to a suitable domain.
Research supported by a Danforth Graduate Fellowship and a Weizmann Postdoctoral Fellowship. 相似文献
6.
All induced connected subgraphs of a graphG contain a dominating set of pair-wise adjacent vertices if and only if there is no induced subgraph isomorphic to a path
or a cycle of five vertices inG. Moreover, the problem of finding any given type of connected dominating sets in all members of a classG of graphs can be reduced to the graphsG∈G that have a cut-vertex or do not contain any cutsetS dominated by somes∈S.
This research was supported in part by the “AKA” Research Fund of the Hungarian Academy of Sciences. 相似文献
7.
We prove that for every polynomial-like holomorphic mapP, ifaεK (filled-in Julia set) and the componentK
aofK containinga is either a point ora is accessible along a continuous curve from the complement ofK andK
ais eventually periodic, thena is accessible along an external ray. Ifa is a repelling or parabolic periodic point, then the set of arguments of the external rays converging toa is a nonempty closed “rotation set”, finite (ifK
ais not a one point) or Cantor minimal containing a pair of arguments of external rays of a critical point in ℂ. In the Appendix
we discuss constructions via cutting and glueing, fromP to its external map with a “hedgehog”, and backward.
Partially supported by the Edmund Landau Center for Research in Mathematical Analysis, sponsored by the Minerva Foundation
(Germany).
Supported by the Polish KBN Grants 210469101 “Iteracje i Fraktale” and 210909101 “Uklady Dynamiczne”. 相似文献
8.
A stable set in a graph G is a set of pairwise nonadjacent vertices. The problem of finding a maximum weight stable set is one of the most basic ℕℙ-hard
problems. An important approach to this problem is to formulate it as the problem of optimizing a linear function over the
convex hull STAB(G) of incidence vectors of stable sets. Since it is impossible (unless ℕℙ=coℕℙ) to obtain a “concise” characterization of STAB(G) as the solution set of a system of linear inequalities, it is a more realistic goal to find large classes of valid inequalities
with the property that the corresponding separation problem (given a point x
*, find, if possible, an inequality in the class that x
* violates) is efficiently solvable.?Some known large classes of separable inequalities are the trivial, edge, cycle and wheel
inequalities. In this paper, we give a polynomial time separation algorithm for the (t)-antiweb inequalities of Trotter. We then introduce an even larger class (in fact, a sequence of classes) of valid inequalities,
called (t)-antiweb-s-wheel inequalities. This class is a common generalization of the (t)-antiweb inequalities and the wheel inequalities. We also give efficient separation algorithms for them.
Received: June 2000 / Accepted: August 2001?Published online February 14, 2002 相似文献
9.
Gabriel Navarro 《Israel Journal of Mathematics》2002,132(1):277-283
Suppose thatG is a finitep-solvable group and letPε Syl
p
(G). In this note, we prove that the character table ofG determines ifN
G(itP)/P is abelian.
Research partially supported by DGICYT. 相似文献
10.
M. E. Dudkin 《Ukrainian Mathematical Journal》1998,50(6):888-900
We give a criterion of invariance and symmetry of the restriction of an arbitrary unbounded self-adjoint operator in the space
L
2(ℝn, dx) by using the introduced notion of support of an arbitrary vector and the notion of capacity of a subspace N ⊂ ℝn.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 781–791, June, 1998.
This work was partially supported by the Foundation for Fundamental Research of the Ministry of Science and Technology of
the Ukraine (grant No. 1/238 “Operator”). 相似文献
11.
Dorothy Maharam 《Israel Journal of Mathematics》1997,98(1):15-28
Let (X, A) be a set with a countably σ-generated “Borel” field of subsets; letW be a “Borel” subset of the product of (X, A) with the real line ℝ and its Borel fieldB; and for eachx∈X let γ
x
be a measure on the “slice”W
x={(w, t)∈W:w=x}. It is shown that, under reasonable conditions, the σ-field A⊗B|W can be generated by a real-valued functiong in such a way that, given any measurablef:W→ℝ,g can be chosen to be arbitrarily close tof and so that its “slice-integrals”
coincide with those off. This theorem is the first step in a study of monotonic sequences of countably generated σ-fields. 相似文献
12.
Gerhard Röhrle 《manuscripta mathematica》1999,98(1):9-20
For a linear algebraic group G over an algebraically closed field k and a parabolic subgroup P of G the modality of P is defined to be the maximal number of parameters upon which a family of G-orbits on Lie P
u
depends and it is denoted by mod P, where P
u
is the unipotent radical of P. The principal aim of this note is a generalization of two basic “monotonicity” results from [19] to positive characteristic:
(1) If Θ is a semisimple automorphism of G and P is Θ-stable, then mod P
\Θ≤ mod P. (2) If G is reductive, char k is a good prime for G, and H is a closed reductive subgroup of G normalized by a maximal torus T⊂P of G, then mod (P∩H)≤ mod P.
Received: 22 April 1998 / Revised version: 3 July 1998 相似文献
13.
We revisit the boundedness of Hankel and Toeplitz operators acting on the Hardy space H
1 and give a new proof of the old result stating that the Hankel operator H
a
is bounded if and only if a has bounded logarithmic mean oscillation. We also establish a sufficient and necessary condition for H
a
to be compact on H
1. The Fredholm properties of Toeplitz operators on H
1 are studied for symbols in a Banach algebra similar to C + H
∞ under mild additional conditions caused by the differences in the boundedness of Toeplitz operators acting on H
1 and H
2.
The first author was partially supported by the European Commission IHP Network “Harmonic Analysis and Related Problems” (Contract
Number: HPRN-CT-2001-00273-HARP) and by the Greek Research Program “Pythagoras 2” (75% European funds and 25 National funds).
The second author was fully supported by the European Commission IHP Network “Harmonic Analysis and Related Problems” (Contract
Number: HPRN-CT-2001-00273-HARP) while he visited the first author at the University of Crete and later by the Academy of
Finland Project 207048. 相似文献
14.
In this paper we show that every sequence (F
n
) of finite dimensional subspaces of a real or complex Banach space with increasing dimensions can be “refined” to yield an
F.D.D. (G
n
), still having increasing dimensions, so that either every bounded sequence (x
n
), withx
n
∈G
n
forn∈ℕ, is weakly null, or every normalized sequence (x
n
),withx
n
∈G
n
forn∈ℕ, is equivalent to the unit vector basis of ℓ1.
Crucial to the proof are two stabilization results concerning Lipschitz functions on finite dimensional normed spaces. These
results also lead to other applications. We show, for example, that every infinite dimensional Banach spaceX contains an F.D.D. (F
n
),with lim
n→∞dim(F
n
)=∞, so that all normalized sequences (x
n
),withx
n
∈F
n
,n∈∕, have the same spreading model overX. This spreading model must necessarily be 1-unconditional overX.
Research partially supported by NSF DMS-8903197, DMS-9208482, and TARP 235.
Research partially supported by NSF. 相似文献
15.
Arthur W. Apter 《Israel Journal of Mathematics》1988,61(3):256-270
In this paper, we construct a modelN in which ℵ1, the only regular uncountable cardinal, is measurable via the club filter. Thus,N is a model for the theory “ZF+κ is regular iffκ is measurable”.
This research in this paper was partially supported by NSF Grant DMS-8413736. 相似文献
16.
Assume that G is a 3-colourable connected graph with e(G) = 2v(G) −k, where k≥ 4. It has been shown that s
3(G) ≥ 2
k
−3, where s
r
(G) = P(G,r)/r! for any positive integer r and P(G, λ) is the chromatic polynomial of G. In this paper, we prove that if G is 2-connected and s
3(G) < 2
k
−2, then G contains at most v(G) −k triangles; and the upper bound is attained only if G is a graph obtained by replacing each edge in the k-cycle C
k
by a 2-tree. By using this result, we settle the problem of determining if W(n, s) is χ-unique, where W(n, s) is the graph obtained from the wheel W
n
by deleting all but s consecutive spokes.
Received: January 29, 1999 Final version received: April 8, 2000 相似文献
17.
LetK be any field of characteristicp>0 and letG be a finite group acting onK via a map τ. The skew group algebraK
τG may be nonsemisimple (precisely whenP|(H), H=Kert). In [1] necessary conditions were given for the existence of a class α∈H
2(G,K*) which “twists” the skew group algebraK
τG into a semisimple crossed productK
τ
αG
. The “twisting problem” asks whether these conditions are sufficient. In [1] we showed that this is indeed so in many cases.
In this paper we prove it in general.
During the period of this research the second author was an Associate at the Center for Advanced Study, Urbana, Illinois. 相似文献
18.
LetG be a unimodular Lie group, Γ a co-compact discrete subgroup ofG and ‘a’ a semisimple element ofG. LetT
a be the mapgΓ →ag Γ:G/Γ →G/Γ. The following statements are pairwise equivalent: (1) (T
a, G/Γ,θ) is weak-mixing. (2) (T
a, G/Γ) is topologically weak-mixing. (3) (G
u, G/Γ) is uniquely ergodic. (4) (G
u, G/Γ,θ) is ergodic. (5) (G
u, G/Γ) is point transitive. (6) (G
u, G/Γ) is minimal. If in additionG is semisimple with finite center and no compact factors, then the statement “(T
a, G/Γ,θ) is ergodic” may be added to the above list.
The authors were partially supported by NSF grant MCS 75-05250. 相似文献
19.
Let (P,≤) be a partially ordered set. The poset Boolean algebra of P, denoted F(P), is defined as follows: The set of generators of F(P) is {x
p
: p∈P}, and the set of relations is {x
p
⋅x
q
=x
p
: p≤q}. We say that a Boolean algebra B is well-generated, if B has a sublattice G such that G generates B and (G,≤
B
|G) is well-founded. A well-generated algebra is superatomic.
THEOREM 1. Let (P,≤) be a partially ordered set. The following are equivalent. (i) P does not contain an infinite set of pairwise incomparable elements, and P does not contain a subset isomorphic to the chain of rational numbers, (ii) F(P) is superatomic, (iii) F(P) is well-generated.
The equivalence (i) ⇔ (ii) is due to M. Pouzet. A partially ordered set W is well-ordered, if W does not contain a strictly decreasing infinite sequence, and W does not contain an infinite set of pairwise incomparable elements.
THEOREM 2. Let F(P) be a superatomic poset algebra. Then there are a well-ordered set W and a subalgebra B of F(W), such that F(P) is a homomorphic image of B.
This is similar but weaker than the fact that every interval algebra of a scattered chain is embeddable in an ordinal algebra.
Remember that an interval algebra is a special case of a poset algebra.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
Let M be an irreducible, orientable, closed 3-manifold with fundamental group G. We show that if the pro-p completion
of G is infinite then G is either soluble-by-finite or contains a free subgroup of rank 2.
Both authors are partially supported by “Bolsa de produtividade de pesquisa” from CNPq, Brazil.
Received: 16 February 2006 相似文献