共查询到20条相似文献,搜索用时 19 毫秒
1.
2.
Claire Anantharaman-Delaroche 《Israel Journal of Mathematics》2003,137(1):1-33
We show that a measuredG-space (X, μ), whereG is a locally compact group, is amenable in the sense of Zimmer if and only if the following two conditions are satisfied:
the associated unitary representationπ
X ofG intoL
2(X, μ) is weakly contained into the regular representationλ
G and there exists aG-equivariant norm one projection fromL∞(X×X) ontoL∞(X). We give examples of ergodic discrete group actions which are not amenable, althoughπ
X is weakly contained intoλ
G. 相似文献
3.
Stefan Bauer 《Commentarii Mathematici Helvetici》1989,64(1):167-172
LetG be a finite group andX an equivariantZ/|G|-homology sphere. By Smith-theory the fixed point setX
H
for ap-subgroupH is aZ/p-homology sphere of dimensiond(H). 相似文献
4.
We consider the problem of constructing a graphG* from a collection of isomorphic copies of a graphG in such a way that for every two copies ofG, either no vertices or a section graph isomorphic to a graphH is identified. It is shown that ifG can be partitioned into vertex-disjoint copies ofH, thenG* can be made to have at most |H| orbits. A condition onG so thatG* can be vertextransitive is also included. 相似文献
5.
Chong-Keang Lim 《Journal of Combinatorial Theory, Series B》1978,24(2):242-246
A given group G may or may not have the property that there exists a graph X such that the automorphism group of X is regular, as a permutation group, and isomorphic to G. Mark E. Watkins has shown that the direct product of two finite groups has this property if each factor has this property and both factors are different from the cyclic group of order 2. Later, Wilfried Imrich generalized this result to infinite groups. In this paper, a new proof of this result for finite groups is given. The proof rests heavily on the result which states that if X is a graphical regular representation of the group G, then X is not self-complementary. 相似文献
6.
G. A. Garkusha 《Journal of Mathematical Sciences》2004,120(4):1561-1562
It is proved that a group ring R = AG is almost regular if and only if (i) the ring A is almost regular; (ii) the group G is locally finite; (iii) the order |H| of every finite subgroup H of G is invertible in A. Bibliography: 7 titles. 相似文献
8.
A. Hajnal 《Israel Journal of Mathematics》1991,73(3):309-319
We prove that for any cardinalτ and for any finite graphH there is a graphG such that for any coloring of the pairs of vertices ofG withτ colors there is always a copy ofH which is an induced subgraph ofG so that both the edges of the copy and the edges of the complement of the copy are monochromatic.
Research supported by Hungarian National Science Foundation OTKA grant 1805. 相似文献
9.
It is shown that every H
-group G of type admits a finite dimensional G-CW-complex X with finite stabilizers and with the additional property that for each finite subgroup H, the fixed point subspace X
H
is contractible. This establishes conjecture (5.1.2) of [9]. The construction of X involves joining a family of spaces parametrized by the poset of non-trivial finite subgroups of G and ultimately relies on the theorem of Cornick and Kropholler that if M is a -module which is projective as a -module for all finite then M has finite projective dimension.
Received: April 30, 1997 相似文献
10.
Let X be a tree and let G=Aut(X), Bass and Tits have given an algorithm to construct the ‘ultimate quotient’ of X by G starting with any quotient of X, an ‘edge-indexed’ graph. Using a sequence of integers that we compute at consecutive steps of the Bass-Tits (BT) algorithm, we give a lower bound on the diameter of the ultimate quotient of a tree by its automorphism group. For a tree X with finite quotient, this gives a lower bound on the minimum number of generators of a uniform X-lattice whose quotient graph coincides with G?X. This also gives a criterion to determine if the ultimate quotient of a tree is infinite. We construct an edge-indexed graph (A,i) for a deterministic finite state automaton and show that the BT algorithm for computing the ultimate quotient of (A,i) coincides with state minimizing algorithm for finite state automata. We obtain a lower bound on the minimum number of states of the minimized automaton. This gives a new proof that language for the word problem in a finitely generated group is regular if and only if the group is finite, and a new proof that the language of the membership problem for a subgroup is regular if and only if the subgroup has finite index. 相似文献
11.
We associate a graph Γ G to a nonlocally cyclic group G (called the noncyclic graph of G) as follows: take G\ Cyc(G) as vertex set, where Cyc(G) = {x ? G| 〈x, y〉 is cyclic for all y ? G}, and join two vertices if they do not generate a cyclic subgroup. We study the properties of this graph and we establish some graph theoretical properties (such as regularity) of this graph in terms of the group ones. We prove that the clique number of Γ G is finite if and only if Γ G has no infinite clique. We prove that if G is a finite nilpotent group and H is a group with Γ G ? Γ H and |Cyc(G)| = |Cyc(H)| = 1, then H is a finite nilpotent group. We give some examples of groups G whose noncyclic graphs are “unique”, i.e., if Γ G ? Γ H for some group H, then G ? H. In view of these examples, we conjecture that every finite nonabelian simple group has a unique noncyclic graph. Also we give some examples of finite noncyclic groups G with the property that if Γ G ? Γ H for some group H, then |G| = |H|. These suggest the question whether the latter property holds for all finite noncyclic groups. 相似文献
12.
LetX
G,H denote the Cayley graph of a finite groupG with respect to a subsetH. It is well-known that its automorphism groupA(XG,H) must contain the regular subgroupL
G corresponding to the set of left multiplications by elements ofG. This paper is concerned with minimizing the index [A(XG,H)LG] for givenG, in particular when this index is always greater than 1. IfG is abelian but not one of seven exceptional groups, then a Cayley graph ofG exists for which this index is at most 2. Nearly complete results for the generalized dicyclic groups are also obtained. 相似文献
13.
Hung P. Tong-Viet 《Monatshefte für Mathematik》2012,15(2):559-577
Let G be a finite group. Denote by Irr(G) the set of all irreducible complex characters of G. Let cd(G)={c(1) | c ? Irr(G)}{{\rm cd}(G)=\{\chi(1)\;|\;\chi\in {\rm Irr}(G)\}} be the set of all irreducible complex character degrees of G forgetting multiplicities, and let X1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Let H be any non-abelian simple exceptional group of Lie type. In this paper, we will show that if S is a non-abelian simple group and cd(S) í cd(H){{\rm cd}(S)\subseteq {\rm cd}(H)} then S must be isomorphic to H. As a consequence, we show that if G is a finite group with X1(G) í X1(H){{\rm X}_1(G)\subseteq {\rm X}_1(H)} then G is isomorphic to H. In particular, this implies that the simple exceptional groups of Lie type are uniquely determined by the structure of their complex group algebras. 相似文献
14.
《代数通讯》2013,41(7):3287-3293
Abstract For an element a of a group G,let S(a) denote the semigroup generated by all conjugates of a in G. We prove that if G is solvable of finite rank and 1 ? S(a) for all 1 ≠ a ∈ G,then ?a G ?/?b G ? is a periodic group for every b ∈ S(a). Conversely if every two generator subgroup of a finitely generated torsion-free solvable group G has this property then G has finite rank,and if every finitely generated subgroup has this property then every partial order on G can be extended to a total order. 相似文献
15.
Luis Paris 《Mathematische Annalen》2002,322(2):301-315
Let G be a countable discrete group. Call two subgroups and of G commensurable if has finite index in both and . We say that an action of G on a discrete set X has noncommensurable stabilizers if the stabilizers of any two distinct points of X are not commensurable. We prove in this paper that the action of the map
ping class group on the complex of curves has noncommensurable stabilizers. Following a method due to Burger and de la Harpe,
this action leads to constructions of irreducible unitary representations of the mapping class group.
Received: 26 July 1999 / Revised version: 14 May 2001 / Published online: 19 October 2001 相似文献
16.
The power graph of a group is the graph whose vertex set is the group, two elements being adjacent if one is a power of the other. We observe that non-isomorphic finite groups may have isomorphic power graphs, but that finite abelian groups with isomorphic power graphs must be isomorphic. We conjecture that two finite groups with isomorphic power graphs have the same number of elements of each order. We also show that the only finite group whose automorphism group is the same as that of its power graph is the Klein group of order 4. 相似文献
17.
V. N. Berestovskii 《Mathematical Notes》1995,58(3):905-909
We prove that a homogeneous effective spaceM=G/H, whereG is a connected Lie group andH⊂G is a compact subgroup, admits aG-invariant Riemannian metric of positive Ricci curvature if and only if the spaceM is compact and its fundamental group π1(M) is finite (in this case any normal metric onG/H is suitable). This is equivalent to the following conditions: the groupG is compact and the largest semisimple subgroupLG⊂G is transitive onG/H. Furthermore, ifG is nonsemisimple, then there exists aG-invariant fibration ofM over an effective homogeneous space of a compact semisimple Lie group with the torus as the fiber.
Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 334–340, September, 1995. 相似文献
18.
A graphH divides a graphG, writtenH|G, ifG isH-decomposable. A graphG without isolated vertices is a greatest common divisor of two graphsG
1 andG
2 ifG is a graph of maximum size for whichG|G
1 andG|G
2, while a graphH without isolated vertices is a least common multiple ofG
1 andG
2 ifH is a graph of minimum size for whichG
1|H andG
2|H. It is shown that every two nonempty graphs have a greatest common divisor and least common multiple. It is also shown that the ratio of the product of the sizes of a greatest common divisor and least common multiple ofG
1 andG
2 to the product of their sizes can be arbitrarily large or arbitrarily small. Sizes of least common multiples of various pairsG
1,G
2 of graphs are determined, including when one ofG
1 andG
2 is a cycle of even length and the other is a star.G. C's research was supported in part by the Office of Naval Research, under Grant N00014-91-I-1060 相似文献
19.
G be a nonabelian torsion-free group. Let C be a finite generating subset of G such that . We prove that, for all subsets B of G with , we have .
In particular, a finite subset X with cardinality satisfies the inequality if and only if there are elements , such that the following two conditions hold:
(i) .
(ii) where .
Received: October 13, 1997/Revised: Revised August 18, 1998 相似文献
20.
Agraph G is a diameter graph in ?d if its vertex set is a finite subset in ?d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in ?4 contains the complete subgraph K on five vertices, then any triangle in G shares a vertex with K. The geometric interpretation of this statement is as follows. Given any regular unit simplex on five vertices and any regular unit triangle in ?4, then either the simplex and the triangle have a common vertex or the diameter of the union of their vertex sets is strictly greater than 1.
相似文献