共查询到20条相似文献,搜索用时 0 毫秒
1.
Benjamin Fine Olga G. Kharlampovich Alexei G. Myasnikov Vladimir N. Remeslennikov G. Rosenberger 《代数通讯》2013,41(8):3386-3394
We prove that the automorphism group of a finitely generated fully residually free group is tame. 相似文献
2.
有限ATI-群的类保持Coleman自同构 总被引:3,自引:3,他引:0
设G是一个有限群,对G的任意阿贝尔子群A及任意g∈G,若A∩A~g=1或A,则称G为一个ATI-群.本文证明了,对任意p∈τ(G),如果ATI-群G的一个p-方幂阶类保持自同构在G的任意Sylow子群上的限制等于G的某个内自同构的限制,则它必定是一个内自同构.作为该结果的一个直接推论,我们也证明了有限ATI-群G有正规化性质. 相似文献
3.
Karen Vogtmann 《Geometriae Dedicata》2002,94(1):1-31
This is a survey of recent results in the theory of automorphism groups of finitely-generated free groups, concentrating on results obtained by studying actions of these groups on Outer space and its variations. 相似文献
4.
Paul Schmutz Schaller 《Compositio Mathematica》2000,122(3):243-260
Let M be a hyperbolic surface and (M) its extended mapping class group. We show that (M) is isomorphic to the automorphism group of the following graph G(M). The set of vertices of G(M) is the set S(M) of nonseparating simple closed geodesics of M. Two vertices u and v of S(M) are related by an edge if u and v intersect exactly once in M. The graph G(M) can be thought of as a combinatorial model for M. 相似文献
5.
We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group
is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated
Fuchsian group and of every free-by-finite group is residually finite. 相似文献
6.
Daciberg Gonçalves 《代数通讯》2013,41(2):909-931
We compute the groups Aut(G) and Out(G) where G is a crystallographic group of rank 2, or so-called wallpaper group. 相似文献
7.
Given a symmetric polynomial (x, y) over a perfect field k of characteristic zero, the Galois graph G() is defined by taking the algebraic closure
as the vertex set and adjacencies corresponding to the zeroes of (x, y). Some graph properties of G(), such as lengths of walks, distances and cycles are described in terms of . Symmetry is also considered, relating the Galois group Gal(
/k) to the automorphism group of certain classes of Galois graphs. Finally, an application concerning modular curves classifying pairs of isogeny elliptic curves is revisited. 相似文献
8.
Chemical reaction graphs (for a fixed type of rearrangement) are orbital graphs for transitive permutation representations of symmetric groups, so algebraic combinatorics and group theory are effective tools for studying such properties as their connectivity and automorphisms. For example, we construct orbital graphs (and, hence, reaction graphs) from Cayley diagrams by contracting edges, and use graph-embeddings in surfaces to determine the automorphism groups of these graphs. We apply these ideas to the rearrangements of the P
7
3-
-ion and of bullvalene, together with some purely mathematical examples of reaction graphs. 相似文献
9.
Zahedeh Azhdari 《代数通讯》2013,41(10):4133-4139
Let G be a group and Autc(G) be the group of all central automorphisms of G. We know that in a finite p-group G, Autc(G) = Inn(G) if and only if Z(G) = G′ and Z(G) is cyclic. But we shown that we cannot extend this result for infinite groups. In fact, there exist finitely generated nilpotent groups of class 2 in which G′ =Z(G) is infinite cyclic and Inn(G) < C* = Autc(G). In this article, we characterize all finitely generated groups G for which the equality Autc(G) = Inn(G) holds. 相似文献
10.
We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form × D,where h has infinite order and D is finite. 相似文献
11.
Wojciech Jaworski 《Journal of Theoretical Probability》1997,10(4):967-989
Let G be a noncompact locally compact group. We show that a necessary and sufficient condition in order that G support an adapted probability measure whose concentration functions fail converge to zero is that G be the semidirect product
, where is an automorphism of N contractive modulo a compact subgroup. Any adapted a probability measure whose concentration functions fail to converge to zero has the form =v×1 where v is a probability measure on N. If G is unimodular then the concentration functions of an adapted probability measure fail to converge to zero if and only if is supported on a coset of a compact normal subgroup. 相似文献
12.
Giovanni Falcone 《Geometriae Dedicata》2001,84(1-3):235-244
We introduce minimal polynomials for finite automorphisms of commutative groups and relate them to the exponent of the fixed points and to the reducibility of the group. Some results can be extended to the noncommutative case. 相似文献
13.
Donald L. White 《代数通讯》2013,41(8):2907-2921
Let G be a finite group and let cd (G) be the set of irreducible character degrees of G. The degree graph Δ(G) is the graph whose set of vertices is the set of primes that divide degrees in cd (G), with an edge between p and q if pq divides a for some degree a ? cd (G). We determine the graph Δ(G) for the finite simple groups of types A ?(q) and 2 A ? (q 2), that is, for the simple linear and unitary groups. 相似文献
14.
设$G$是一个本原群,证明了存在某个素数$p$使得$G$的每个$p$-中心自同构是内自同构. 作为应用,证明了$G$的全形的每个Coleman自同构均为内自同构. 特别地,正规化子性质对对所讨论的这些群都成立. 另外也得到了其他一些相关结果. 相似文献
15.
Carla BARDINI 《数学年刊B辑(英文版)》2012,33(5):783-800
The author studies the linkage between the standardness and the standard automorphisms of Chevalley groups over rings.It is proved that if H is any standard subgroup of G(R),then each of its automorphisms can be extended to an automorphism of G(R,I),restricted to an automorphism of E(R,I),and an automorphism of E(R,I) can be extended to one of G(R,I).The case of Chevalley groups of rank at least two is treated in this paper.Further results about the case of Chevalley groups of rank one,the case of non-commutative ground ring and some others exceptions will appear elsewhere. 相似文献
16.
17.
Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the -regular graphs
associated to regular tessellations of the hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs are Salem numbers. We also prove that these denominators are essentially irreducible (they have a factor of X + 1 when m 2 mod 4; and when = 3 and m 4 mod 12, for instance, they have a factor of X
2 – X + 1). We then derive some regularity properties for the coefficients f
n
of the growth series: they satisfy K
n
– R < f
n
< K
n
+ R for some constants K, R < 0, < 1. 相似文献
18.
Jiří Rachůnek 《Order》2001,18(4):349-357
By the Holland Representation Theorem, every lattice ordered group (l-group) is isomorphic to a subalgebra of the l-group of automorphisms of a chain. Since weakly associative lattice groups (wal-groups) and tournaments are non-transitive generalizations of l-groups and chains, respectively, the problem concerning the possibility of representation of wal-groups by automorphisms of tournaments arises. In the paper we describe the class of wal-groups isomorphic to wal-groups of automorphisms of tournament and show some of its properties. 相似文献
19.
《代数通讯》2013,41(9):3641-3649
Abstract Let G be a finite group and let cd(G) be the set of irreducible character degrees of G. The degree graph Δ(G) of G is the graph whose set of vertices is the set of primes that divide degrees in cd(G), with an edge between p and q if pq divides a for some degree a ∈ cd(G). In this paper, we determine the graph Δ(G) when G is a finite simple group of exceptional Lie type. 相似文献
20.
广义四元数群的4-度Cayley图 总被引:1,自引:0,他引:1
一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3.本文根据广义四元数群Q4p(p为奇素数)中只有两类二元生成子集,且它们在Aut(Q4p)的作用下是传递的.结合具体图形,利用查圈的方法重点地证明了广义四元数群关于这两类二元生成子集的4-度C ay ley图的正规性与正则性,解决了4-度C ay ley图的完全分类问题. 相似文献