首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 31 毫秒
1.
A subgroup of a pro-p product with amalgamation of two p-groups is given which cannot be presented as the pro-p fundamental group of a profinite graph of p-groups.  相似文献   

2.
We develop an approach to the character theory of certain classes of finite and profinite groups based on the construction of a Lie algebra associated to such a group, but without making use of the notion of a polarization which is central to the classical orbit method. Instead, Kirillov’s character formula becomes the fundamental object of study. Our results are then used to produce an alternate proof of the orbit method classification of complex irreducible representations of p-groups of nilpotence class < p, where p is a prime, and of continuous complex irreducible representations of uniformly powerful pro-p-groups (with a certain modification for p = 2). As a main application, we give a quick and transparent proof of the p-adic analogue of Brown’s theorem, stating that for a nilpotent Lie group over ℚp the Fell topology on the set of isomorphism classes of its irreducible representations coincides with the quotient topology on the set of its coadjoint orbits. The research of M. B. was partially supported by NSF grant DMS-0401164.  相似文献   

3.
We extend a construction of Higman, Neumann and Neumann [LS, IV.3.1] and show that every profinite groupG with only countably many open subgroups embeds in a 2-generated profinite groupE in which all torsion elements are conjugate to elements ofG; ifG is pro-p,E can be chosen pro-p. This answers a question of Wilson (oral communication) and generalises a result of Lubotzky and Wilson [LW].  相似文献   

4.
A profinite group G of finite cohomological dimension with (topologically)finitely generated closed normal subgroup N is studied. If Gis pro-p and N is either free as a pro-p group or a Poincarégroup of dimension 2 or analytic pro-p, it is shown that G/Nhas virtually finite cohomological dimension cd(G)–cd(N).Some other cases when G/N has virtually finite cohomologicaldimension are also considered. If G is profinite, the case of N projective or the profinitecompletion of the fundamental group of a compact surface isconsidered.  相似文献   

5.
We prove that in the category of pro-p groups any finitely generated group G with a free open subgroup splits either as an amalgamated free product or as an HNN-extension over a finite p-group. From this result we deduce that such a pro-p group is the pro-p completion of a fundamental group of a finite graph of finite p-groups.  相似文献   

6.
We compute the Fp-dimension of an n-th graded piece G(n)/G(n+1) of the Zassenhaus filtration for various finitely generated pro-p-groups G. These groups include finitely generated free pro-p-groups, Demushkin pro-p-groups and their free pro-p products. We provide a unifying principle for deriving these dimensions.  相似文献   

7.
Let G be a group. An element gG is called a test element of G if for every endomorphism ? : GG, ?(g) = g implies ? is an automorphism. We prove that for a finitely generated profinite group G, gG is a test element of G if and only if it is not contained in a proper retract of G. Using this result we prove that an endomorphism of a free pro-p group of finite rank which preserves an automorphic orbit of a nontrivial element must be an automorphism. We give numerous explicit examples of test elements in free pro-p groups and Demushkin groups. By relating test elements in finitely generated residually finite-p Turner groups to test elements in their pro-p completions, we provide new examples of test elements in free discrete groups and surface groups. Moreover, we prove that the set of test elements of a free discrete group of finite rank is dense in the profinite topology.  相似文献   

8.
For a prime number p let G be a profinite p-PD n group with a closed normal subgroup N such that G/N is a profinite p-PD m group and that H i (V, $ \mathbb{F} $ \mathbb{F} p ) is finite for every open subgroup V of N and all i ≤ [n/2]. Generalising [12, Thm. 3.7.4] we show that mn and N is a profinite p-PD n − m group. In case that G is a pro-p PD n group of Euler characteristic 0 with a closed normal subgroup N of type FP [n−1 / 2] such that G/N is soluble-by-finite pro-p group of finite rank, we show that N is a pro-p PD n − m group, where m = vcd p (G/N). As a corollary we obtain that a pro-p PD 3 group with infinite abelianization is either soluble or contains a free nonprocyclic pro-p subgroup.  相似文献   

9.
A major difficult problem in Galois theory is the characterization of profinite groups which are realizable as absolute Galois groups of fields. Recently the Kernel n-Unipotent Conjecture and the Vanishing n  -Massey Conjecture for n≥3n3 were formulated. These conjectures evolved in the last forty years as a byproduct of the application of topological methods to Galois cohomology. We show that both of these conjectures are true for odd rigid fields. This is the first case of a significant family of fields where both of the conjectures are verified besides fields whose Galois groups of p-maximal extensions are free pro-p-groups. We also prove the Kernel Unipotent Conjecture for Demushkin groups of rank 2, and establish various filtration results for free pro-p-groups, provide examples of pro-p-groups which do not have the kernel n-unipotent property, compare various Zassenhaus filtrations with the descending p-central series and establish new type of automatic Galois realization.  相似文献   

10.
We consider profinite groups in which all commutators are contained in a union of finitely many procyclic subgroups. It is shown that if G is a profinite group in which all commutators are covered by m procyclic subgroups, then G possesses a finite characteristic subgroup M contained in G′ such that the order of M is m-bounded and G′/M is procyclic. If G is a pro-p group such that all commutators in G are covered by m procyclic subgroups, then G′ is either finite of m-bounded order or procyclic.  相似文献   

11.
Letp be a prime number,G a pro-p group, andH a closed (topologically) finitely generated subgroup ofG. We give conditions under whichH is virtually a free factor ofG, i.e., that there exists an open subgroupU ofG such thatU is the free pro-p product ofH and some other subgroup ofU. We prove that this happens if eitherG is a free pro-p group of any rank, or ifG is a free pro-p product of finitely generated pro-p groups. Research supported in part by grants from NSERC (Canada) and DGICYT (Spain).  相似文献   

12.
It is shown that every profinite torsion group has a finite series of closed characteristic subgroups in which each factor either is a pro-p-group for some primep or is isomorphic to a Cartesian product of isomorphic finite simple groups.  相似文献   

13.
This paper is devoted to the first steps towards a systematic study of pro-p groups which are analytic over a commutative Noetherian local pro-p ring Λ, e.g. Λ= . We restrict our attention to Λ-standard groups, which are pro-p groups arising from a formal group defined over Λ. Under some additional assumptions we show that these groups are of ‘intermediate growth’ in various senses, strictly betweenp-adic analytic pro-p groups and free pro-p groups. This suggests a refinement of Lazard's theory which stresses the dichotomy betweenp-adic analytic pro-p groups and all the others. In the course of the discussion we answer a question posed in [LM1], and settle two conjectures from [Bo].  相似文献   

14.
The object of this paper is to construct outer automorphisms for nilpotent torsion-free profinite groups, what reduces to nilpotent compact torsion-free pro-p-groups. If the class of such a group is greater than 2, a characteristic subgroupA can be found, such that the stabilizer of the series 1AC G (A)G in AutG contains a subgroup which modulo InnG is isomorphic to the center ofG. A similar result is obtained for class 2 groups with some exception for which AutG is given explicitely. In course of the proof for the class 2 case, the group Hom (A, B) of continuous homomorphisms is analysed, whereA is a locally direct product of a family {A i ;iI} and allA i 's andB are locally compact abelian groups.  相似文献   

15.
A group G is said to be rigid if it contains a normal series of the form G = G 1 > G 2 > … > G m  > G m + 1 = 1, whose quotients G i /G i + 1 are Abelian and are torsion free as right Z[G/G i ]-modules. In studying properties of such groups, it was shown, in particular, that the above series is defined by the group uniquely. It is known that finitely generated rigid groups are equationally Noetherian: i.e., for any n, every system of equations in x 1, …, x n over a given group is equivalent to some of its finite subsystems. This fact is equivalent to the Zariski topology being Noetherian on G n , which allowed the dimension theory in algebraic geometry over finitely generated rigid groups to have been constructed. It is proved that every rigid group is equationally Noetherian. Supported by RFBR (project No. 09-01-00099) and by the Russian Ministry of Education through the Analytical Departmental Target Program (ADTP) “Development of Scientific Potential of the Higher School of Learning” (project No. 2.1.1.419). Translated from Algebra i Logika, Vol. 48, No. 2, pp. 258–279, March–April, 2009.  相似文献   

16.
Ido Efrat 《代数通讯》2013,41(6):2999-3021
For non-archimedean local field K and a prime number p we compute the finitely generated pro-p (closed) subgroups of the absolute Galois group of K(t). In addition, we characterize the finitely generated pro-p groups which occur as the maximal pro-p Galois group of algebraic extensions of K(t) containing a primitive pth root of unity.  相似文献   

17.
In this text, we study Kirillov's orbit method in the context of Lazard's p-saturable groups when p is an odd prime. Using this approach we prove that the orbit method works in the following cases: torsion free p-adic analytic pro-p groups of dimension smaller than p, pro-p Sylow subgroups of classical groups over ? p of small dimension and for certain families of finite p-groups.  相似文献   

18.
We prove that a 2-group has exactly five rational irreducible characters if and only if it is dihedral, semidihedral or generalized quaternion. For an arbitrary prime p, we say that an irreducible character χ of a p-group G is “almost rational” if ℚ(χ) is contained in the cyclotomic field ℚ p , and we write ar(G) to denote the number of almost-rational irreducible characters of G. For noncyclic p-groups, the two smallest possible values for ar(G) are p 2 and p 2 + p − 1, and we study p-groups G for which ar(G) is one of these two numbers. If ar(G) = p 2 + p − 1, we say that G is “exceptional”. We show that for exceptional groups, |G: G′| = p 2, and so the assertion about 2-groups with which we began follows from this. We show also that for each prime p, there are exceptional p-groups of arbitrarily large order, and for p ≥ 5, there is a pro-p-group with the property that all of its finite homomorphic images of order at least p 3 are exceptional.  相似文献   

19.
LetG be a profinite group which has an open subgroupH such that the cohomologicalp-dimensiond≔cdp(H) is finite (p is a fixed prime). The main result of this paper expresses thep-primary part of high degree cohomology ofG in terms of the elementary abelianp-subgroups ofG: From the latter one constructs a natural profinite simplicial setA G, on whichG acts by conjugation. ThenH n(G,M)≅H G n (AG,M) holds fornd+r and everyp-primary discreteG-moduleM (rp-rank ofG). If one uses profinite Farrell cohomology, which is introduced in this paper, the analogous fact holds in all degrees. These results are the profinite analogues of theorems by K.S. Brown for discrete groups.  相似文献   

20.
Let G be a finitely presented pro- C{\cal C} group with discrete relations. We prove that the kernel of an epimorphism of G to [^(\Bbb Z)]C\hat{\Bbb Z}_{\cal C} is topologically finitely generated if G does not contain a free pro- C{\cal C} group of rank 2. In the case of pro-p groups the result is due to J. Wilson and E. Zelmanov and does not require that the relations are discrete ([15], [17]).For a pro-p group G of type FPm we define a homological invariant C{\cal C} groups, pro-p groups, homological type FPm, finite presentabilityBoth authors are partially supported by CNPq, Brazil.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号