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1.
A proper subgroup H of a group G is said to be strongly embedded if 2 (H) and 2(HH
g) (for all
). An involution i of G is said to be finite if
(for all g G). As is known, the structure of a (locally) finite group possessing a strongly embedded subgroup is determined by the theorems of Burnside and Brauer--Suzuki, provided that the Sylow 2-subgroup contains a unique involution. In this paper, sufficient conditions for the equality m
2(G)= 1 are established, and two analogs of the Burnside and Brauer—Suzuki theorems for infinite groups G possessing a strongly embedded subgroup and a finite involution are given. 相似文献
2.
Suppose that is the set of connected graphs such that a graph G if and only if G satisfies both (F1) if X is an edge cut of G with |X|3, then there exists a vertex v of degree |X| such that X consists of all the edges incident with v in G, and (F2) for every v of degree 3, v lies in a k-cycle of G, where 2k3.In this paper, we show that if G and (G)3, then for every pair of edges e,fE(G), G has a trail with initial edge e and final edge f which contains all vertices of G. This result extends several former results. 相似文献
3.
N. G. Khisamiev 《Algebra and Logic》2002,41(4):274-283
Let G be a completely decomposable torsion-free Abelian group and G= Gi, where G
i
is a rank 1 group. If there exists a strongly constructive numbering of G such that (G,) has a recursively enumerable sequence of elements g
i
G
i
, then G is called a strongly decomposable group. Let pi, i, be some sequence of primes whose denominators are degrees of a number p
i
and let
. A characteristic of the group A is the set of all pairs ‹ p,k› of numbers such that
for some numbers i
1,...,i
k
. We bring in the concept of a quasihyperhyperimmune set, and specify a necessary and sufficient condition on the characteristic of A subject to which the group in question is strongly decomposable. Also, it is proved that every hyperhyperimmune set is quasihyperhyperimmune, the converse being not true. 相似文献
4.
One considers the class
G
of holomorphic functions in a domain G, whose values are contractions in a separable Hilbert space. It is proved that if T(·)
G
, T(z0) is a weak contraction, its singular part Ts(z0) is complete, and the increments T(z)–T(z0) are not too large (for example, finite-dimensional), then the operator Ts(z0) is complete for almost all zG. If, however, T(z0) is, in addition, completely nonunitary and satisfies definite smoothness conditions, then in the nontrivial case the spectrum [z] of the contraction Ts(z) (zG) is a thin set: The proof of the mentioned results is based on the investigation of the formulas obtained in the paper, connecting the characteristic functions of the contractions T(z) for different values of zG.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 30–44, 1987. 相似文献
5.
Let G be a simple graph. A subset S V is a dominating set of G, if for any vertex v V – S there exists a vertex u S such that uv E(G). The domination number, denoted by (G), is the minimum cardinality of a dominating set. In this paper we prove that if G is a 4-regular graph with order n, then (G) 4/11 n 相似文献
6.
Luigi Antonio Rosati 《Geometriae Dedicata》1987,24(3):261-267
Summary Let G be a sharply 3-transitive permutation set on a finite set E of even cardinality and let 1 be in G. The following theorems are proved.
G is one of the known examples if and only if there exists a non-identity normal subgroup N of G and an element of E such that NG
G.G is a group if and only if G for every G and for every G and for every G
.By using the classification of finite single groups a result concerning sharply k-transitive permutation sets k>3 is also proved.
Dedicato a Guido Zappa in occasione del suo 70° compleanno
Lavoro eseguito nell'ambito dei progetti finanziati dal Ministero della Pubblica Istruzione. 相似文献
Dedicato a Guido Zappa in occasione del suo 70° compleanno
Lavoro eseguito nell'ambito dei progetti finanziati dal Ministero della Pubblica Istruzione. 相似文献
7.
Piotr Bugiel 《Monatshefte für Mathematik》1992,113(4):255-263
A class of uniformly expanding, piecewiseC
2-diffeomorphisms from domainsIR
d
(bounded or not) into themselves is considered. It is shown that the number of the extreme points of Fix (P
)={gG:Pg=g} whereP
is the Frobenius-Perron operator associated with andG={gL
1: g0 g=1}, can be determined in an effective way. Moreover, it is shown that the sequence {P
j
g} is convergent inL
1 for anygG, and in the topology of uniform convergence for anygG(1). The limit is a linear projectionR inL
1 (defined by (3.1)) which mapsG onto Fix (P
) (see Th. 3.1).Dedicated to professor A. Lasota on the occasion of his 60th birthday 相似文献
8.
P. N. Müller K. -D. Reinsch R. Bulirsch 《Journal of Optimization Theory and Applications》1994,80(2):367-372
In Ref. 1, the author claimed that the problem y=y
3 is soluble only for a certain range of the parameter . An analytic approach, as adopted in the following contribution, reveals that a unique solution exists for any positive value of . The solution is given in closed form by means of Jacobian elliptic functions, which can be numerically computed very efficiently. In the limit 0+, the solutions exhibit boundary-layer behavior at both endpoints. An easily interpretable approximate solution for small is obtained using a three-variable approach. 相似文献
9.
Mehdi Khayaty 《Southeast Asian Bulletin of Mathematics》2000,24(2):239-242
Let G be a transitive permutation group on a set and m a positive integer. If | – | m for every subset of and all g G, then || 2mp/(p – 1) where p is the least odd prime dividing |G|. It was shown by Mann and Praeger [13] that, for p = 3, the 3-groups G which attain this bound have exponent p. In this paper we will show a generalization of this result for any odd primes.AMS Subject Classification (2000), 20BXX 相似文献
10.
I. U. Bronshtein 《Mathematical Notes》1969,5(1):49-51
Let G be a topological group, H a closed subgroup of the group G, and G/H a homogeneous space of cosets Hg(g G). The group G acts naturally on G/H, defining a transitive transformation group (G/H, G,gp), (Ha, g)=Hag(a G, g G). Necessary and sufficient conditions for the distalness of the transformation group (G/H, G,) are indicated.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 77–80, January, 1969. 相似文献
11.
For graphsA andB the relationA(B)
r
1
means that for everyr-coloring of the vertices ofA there is a monochromatic copy ofB inA. Forb (G) is the family of graphs which do not embedG. A familyof graphs is Ramsey if for all graphsBthere is a graphAsuch thatA(B)
r
1
. The only graphsG for which it is not known whether Forb (G) is Ramsey are graphs which have a cutpoint adjacent to every other vertex except one. In this paper we prove for a large subclass of those graphsG, that Forb (G) does not have the Ramsey property.This research has been supported in part by NSERC grant 69-1325. 相似文献
12.
Let G be a finite group and
e(G) the set of element orders of G. Denote by h(
e(G)) the number of isomorphism classes of finite groups H satisfying
e(H) =
e(G). We prove that if G has at least three prime graph components, then h(
e
(G)){1, }. 相似文献
13.
Zusammenfassung Gegeben seien endliche MengenX, Y undZ X × Y, Z
x
={y¦(x,y) Z},Z
y
={x¦(x,y) Z}.Man nenntA X (bzw.B Y)zuordenbar, wenn es eine Injektion:A Y (bzw.: B X) mit(x) Z
x
(bzw.(y) Z
y
) gibt, und (A, B) mit #A=#B > 0 einZuordnungspaar, wenn eine Bijektionf:A B mitf(x)Z
x
B (bzw.f
–1
(y) Z
y
A) existiert. Die Bijektionf heißtZuordnungsplan fürA, B.In der vorliegenden Arbeit werden Fragen nach der Existenz von optimal zuordenbaren Mengen und optimalen Zuordnungspaaren behandelt, wenn man auf den MengenX undY Ordnungen vorgibt, wobei auch Nebenbedingungen berücksichtigt werden. In manchen Fällen lassen sich anhand der Beweise Zuordnungspläne oder ihre Berechnungsvorschrift explizit angeben.Zum Schluß werden die Aussagen an konkreten, dem Bereich der Wirtschaftswissenschaften entnommenen Beispielen erläutert.
Diese Arbeit ist mit Unterstützung des Sonderforschungsbereiches 72 an der Universität Bonn entstanden. 相似文献
Summary LetX, Y be finite sets andZ X × Y, Z x ={y¦(x,y) Z},Z y ={x¦(x,y)Z}. A X (resp.B Y) is calledassignable if there is an injection: A Y (resp.: B X) with (x) Z x (resp.(y) Z y ), (A, B) with #A=#B > 0 anassigned pair if there is a bijection f:A B withf (x) Z x B (resp.f –1(y) Z y A). The bijectionf is called aplan forA andB.In this paper problems are discussed concerning the existence of optimal assignable sets and optimal assigned pairs ifX andY are totally ordered, additional constraints are also considered. In some cases the proofs give explicit constructions of plans. The results are illustrated by application to problems occurring in Operations Research.
Diese Arbeit ist mit Unterstützung des Sonderforschungsbereiches 72 an der Universität Bonn entstanden. 相似文献
14.
It is proved that if S, T are two elliptic Dirichlet operators on an ordered Hilbert space such that the excessive (resp. coexcessive) elements with respect to S and T are the same then there exists > 0 with T = S. Particularly if , are two elliptic Dirichlet forms on L2 ( ) having the same domain of definition and the same -excessive (resp. -coexcessive) elements for any > 0 then = . 相似文献
15.
Pham Huu Sach 《Applied Mathematics and Optimization》1990,22(1):189-209
Second-order necessary optimality conditions are established under a regularity assumption for a problem of minimizing a functiong over the solution set of an inclusion system 0 F(x), x M, whereF is a set-valued map between finite-dimensional spaces andM is a given subset. The proof of the main result of the paper is based on the theory of infinite systems of linear inequalities. 相似文献
16.
Given D a domain in
, G an open set in
and E a subset of D verifying the harmonic analogue of Local Polynomial Condition of Leja at some point in D. We prove that if f(x, y) is a complex function defined on D × G such that– f(x, ) is harmonic on G for every fixed x E,– f(, y) is harmonic on D for every fixed y G,then f is harmonic in (x, y) on D × G. 相似文献
17.
18.
Michel Sebille 《Designs, Codes and Cryptography》2001,22(3):215-219
In 1987, Teirlinckproved that if t and are two integers such that v t(mod(t + 1)!(2t+1) and v t + 1 >0, then there exists a t - (v, t + 1, (t + 1)!(2t+1)) design. We prove that if there exists a (t+1)-(v,k,)design and a t-(v-1,k-2, (k-t-1)/(v-k+1))design with t 2, then there exists a t-(v+1,k, (v-t+1)(v-t)/
(v-k+1)(k-t))design. Using this recursive construction, we prove that forany pair (t,n) of integers (t 2and n 0), there exists a simple non trivial t-(v,k,) design having an automorphism groupisomorphic to n
2. 相似文献
19.
Let G be a intransitive permutation group on a set with no fixed point in ; let m, n be a positive integer and let |g – | m, for every
and g G. When G has t orbits and degree n close to [2mp/(p – 1)] + t – 1, this paper constructs such a group with m close to [n(p – 1)/2p].AMS Subject Classification: 20BXX. 相似文献
20.
R. K. Getoor 《Potential Analysis》1995,4(1):79-100
SupposeX is a Borel right process andm is a -finite excessive measure forX. Given a positive measure not chargingm-semipolars we associate an exact multiplicative functionalM(). No finiteness assumptions are made on . Given two such measures and ,M()=M() if and only if and agree on all finely open measurable sets. The equation (q–L)u+u=f whereL is the generator of (a subprocess of)X may be solved for appropriatef by means of the Feynman-Kac formula based onM(). Both uniqueness and existence are considered.Supported in part by NSF Grant DMS 92-24990. 相似文献