共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
3.
D. T. Wise 《Commentarii Mathematici Helvetici》2001,76(2):314-338
It is proven that every positive one-relator group which satisfies the condition has a finite index subgroup which splits as a free product of two free groups amalgamating a finitely generated
malnormal subgroup. As a consequence, it is shown that every positive one-relator group is residually finite. It is shown that positive one-relator groups are generically and hence generically residually finite. A new method is given for recognizing malnormal subgroups of free groups. This method
employs a 'small cancellation theory' for maps between graphs.
Received: August 4, 2000 相似文献
4.
A function ? → ? is near exponential if it is bounded above and below by functions of the form \({2^{{n^c}}}\) for some c > 0. In this article we develop tools to recognize the near exponential residual finiteness growth in groups acting on rooted trees. In particular, we show the near exponential residual finiteness growth for certain branch groups, including the first Grigorchuk group, the family of Gupta–Sidki groups and their variations, and Fabrykowski–Gupta groups. We also show that the family of Gupta–Sidki p-groups, for p ≥ 5, have super-exponential residual finiteness growth. 相似文献
5.
Full residual finiteness growth of a finitely generated group G measures how efficiently word metric n-balls of G inject into finite quotients of G. We initiate a study of this growth over the class of nilpotent groups. When the last term of the lower central series of G has finite index in the center of G we show that the growth is precisely nb, where b is the product of the nilpotency class and dimension of G. In the general case, we give a method for finding an upper bound of the form nb where b is a natural number determined by what we call a terraced filtration of G. Finally, we characterize nilpotent groups for which the word growth and full residual finiteness growth coincide. 相似文献
6.
7.
8.
It is well known that if two algebraic structures A and B are residually finite then so is their direct product. Here we discuss the converse of this statement. It is of course true
if A and B contain idempotents, which covers the case of groups, rings, etc. We prove that the converse also holds for semigroups even
though they need not have idempotents. We also exhibit three examples which show that the converse does not hold in general.
相似文献
9.
D. N. Azarov 《Mathematical Notes》2014,96(1-2):161-165
Let G be a group of finite generic rank, φ an injective endomorphism of the group G, and G(φ) the descending HNN-extension of G corresponding to the endomorphism φ. Let the index of the subgroup Gφ in G be finite and equal to n. It is proved that, if the group G is almost residually π-finite for some set π of primes coprime to n, then the group G(φ) is residually finite. This generalizes a series of known results, including the Wise-Hsu theorem on the residual finiteness of an arbitrary descending HNN-extension of any almost polycyclic group. 相似文献
10.
11.
Daniel T. Wise 《Inventiones Mathematicae》2002,149(3):579-617
A subgroup M⊂G is almost malnormal provided that for each g∈G−M, the intersection M
g
∩M is finite. It is proven that the free product of two virtually free groups amalgamating a finitely generated almost malnormal
subgroup, is residually finite. A consequence of a generalization of this result is that an acute-angled n-gon of finite groups is residually finite if n≥4. Another consequence is that if G acts properly discontinuously and cocompactly on a 2-dimensional hyperbolic building whose chambers have acute angles and
at least 4 sides, then G is residually finite.
Oblatum 17-VII-2000 & 13-II-2002?Published online: 29 April 2002 相似文献
12.
V. Metaftsis 《Journal of Pure and Applied Algebra》2010,214(8):1301-1305
We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable relatively hyperbolic group is residually finite. As a direct consequence, we obtain that the outer automorphism group of a limit group is residually finite. 相似文献
13.
14.
D. N. Azarov 《Siberian Mathematical Journal》2013,54(3):379-387
We find necessary and sufficient conditions for the residual finiteness of some free products of finite rank groups with amalgamated subgroups. 相似文献
15.
Stephen J. Pride 《Proceedings of the American Mathematical Society》2008,136(2):377-386
A relative one-relator presentation has the form where is a set, is a group, and is a word on . We show that if the word on obtained from by deleting all the terms from has what we call the unique max-min property, then the group defined by is residually finite if and only if is residually finite (Theorem 1). We apply this to obtain new results concerning the residual finiteness of (ordinary) one-relator groups (Theorem 4). We also obtain results concerning the conjugacy problem for one-relator groups (Theorem 5), and results concerning the relative asphericity of presentations of the form (Theorem 6).
16.
Faithful linear representations and residual finiteness of some products of cycles with one relation
G. Rosenberg 《Siberian Mathematical Journal》1991,32(1):166-168
Dortmund, Germany. Novosibirsk, USSR. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 1, pp. 204–206, January–February, 1991. 相似文献
17.
We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of affine spaces over finite fields. In particular, we prove that when such a map is dominant, the set of its fixed closed scheme points is Zariski dense in the affine space. 相似文献
18.
On the residual finiteness of the HNN-extensions and generalized free products of finite rank groups
D. N. Azarov 《Siberian Mathematical Journal》2013,54(6):959-967
We obtain necessary and sufficient conditions for the residual finiteness for some HNN-extensions and generalized free products of soluble minimax groups. 相似文献
19.
D. N. Azarov 《Mathematical Notes》2013,93(3-4):503-509
A necessary and sufficient condition for the residual finiteness of a (generalized) free product of two residually finite solvable-by-finite minimax groups with cyclic amalgamated subgroups is obtained. This generalizes the well-known Dyer theorem claiming that every free product of two polycyclic-by-finite groups with cyclic amalgamated subgroups is a residually finite group. 相似文献
20.
Wilderich Tuschmann 《Mathematische Annalen》2002,322(2):413-420
The main results of this note consist in the following two geometric finiteness theorems for diffeomorphism types and homotopy
groups of closed simply connected manifolds:
1. For any given numbers C and D the class of closed smooth simply connected manifolds of dimension which admit Riemannian metrics with sectional curvature bounded in absolute value by $\vert K \vert\le C$ and diameter bounded
from above by D contains at most finitely many diffeomorphism types. In each dimension there exist counterexamples to the preceding statement.
2. For any given numbers C and D and any dimension m there exist for each natural number up to isomorphism always at most finitely many groups which can occur as the k-th homotopy group of a closed smooth simply connected m-manifold which admits a metric with sectional curvature and diameter .
Received: 21 August 1999 / Accepted: 20 April 2001 / Published online: 19 October 2001 相似文献