共查询到20条相似文献,搜索用时 31 毫秒
1.
Peter Davidson 《代数通讯》2013,41(4):1448-1459
Pride groups are defined by means of finite (simplicial) graphs, and examples include Artin groups, Coxeter groups, and generalized tetrahedron groups. Under suitable conditions, we calculate an upper bound of the first order Dehn function for a finitely presented Pride group. We thus obtain sufficient conditions for when finitely presented Pride groups have solvable word problems. As a corollary to our main result, we show that the first order Dehn function of a generalized tetrahedron group, containing finite generalized triangle groups, is at most cubic. 相似文献
2.
Gerald Williams 《代数通讯》2013,41(1):251-258
The class of groups defined by periodic paired relations, as introduced by Vinberg, includes the generalized triangle groups, the generalized tetrahedron groups, and the generalized Coxeter groups. We observe that any group defined by periodic paired relations Γ can be realized as a so-called “Pride group”. Using results of Howie and Kopteva we give necessary and sufficient conditions for this Pride group to be non-spherical. Under such conditions, we show that Γ satisfies the Tits alternative. Communicated by A. Olshanskiy 相似文献
3.
We are interested in the maximum possible number of facets that Dirichlet stereohedra for three-dimensional crystallographic
groups can have. In two previous papers, D. Bochiş and the second author studied the problem for noncubic groups. This paper
deals with “full” cubic groups, while “quarter” cubic groups are left for a subsequent paper. Here, “full” and “quarter” refers
to the recent classification of three-dimensional crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston.
This paper’s main result is that Dirichlet stereohedra for any of the 27 full groups cannot have more than 25 facets. We also
find stereohedra with 17 facets for one of these groups.
Research partially supported by the Spanish Ministry of Education and Science, grant number MTM2005-08618-C02-02. 相似文献
4.
It is well-known that the class of slender groups is closed under extensions, arbitrary direct sums and subgroups. We show
that it is also closed under taking unions of continuous well-ordered ascending chains of groups where each factor of consecutive
groups is slender (Theorem 2.2). We also prove that the class of slender groups cannot be obtained from any set of slender
groups by forming unions of chains of the mentioned kind and taking subgroups (Theorem 4.2). This generalizes a result by
G?bel-Wald [11].
We observe that the same results hold if in the theorems ‘slender’ is replaced by ‘reduced torsion-free’ or ‘cotorsion-free’.
Received: 30 June 2005 相似文献
5.
Integrated Groups and Smooth Distribution Groups 总被引:1,自引:0,他引:1
Pedro J. MIANA 《数学学报(英文版)》2007,23(1):57-64
In this paper, we prove directly that α-times integrated groups define algebra homomorphisms. We also give a theorem of equivalence between smooth distribution groups and α-times integrated groups. 相似文献
6.
We show how the finite symplectic groups arise as quotients of the pure symplectic braid group. Via [SV] certain of these
groups — in particular, all groups Sp
n
(2) — occur as Galois groups over ℚ.
Supported by NSF grant DMS-9306479. 相似文献
7.
8.
Paul C. Eklof 《Israel Journal of Mathematics》1976,25(1-2):97-107
The paper is a survey of results in the model theory of abelian groups, dealing with two sorts of problems: finding invariants
which classify groups up toL
λκ-equivalence; and determining whether certain classes of groups are definable inL
λκ.
Research supported by NSF grant GP 43910 相似文献
9.
Let ℱ be an homomorph and Fitting class such thatE
zℱ=ℱ. In this paper we prove that if all ℱ-constrained groups have ℱ-injectors, then all groups have ℱ-injectors. In particular
if ℱ is a class of quasinilpotent groups containing the nilpotent groups, then every group has ℱ-injectors. 相似文献
10.
Benjamin Klopsch 《Israel Journal of Mathematics》2003,137(1):265-284
Let Σ denote the class of allnon-abelian finite simple groups. We are concerned with enumerating poly-Σ groups, that is finite groups without abelian composition
factors. For any natural numbern let gΣ(n) denote the number of (isomorphism classes of) poly-Σ groups of order at mostn. We determine the growth rate of the sequence gΣ(n),n ε ℵ.
Similarly, for anyS ε Σ we give estimates for the numbers ĝS(k) of poly-S groups of composition length at mostk, ask tends to infinity. This initiates an investigation somewhat complementary to the “classical” enumeration of finitep-groups by Higman [6] and Sims [15].
Our ancillary results include upper bounds for the minimal number of generators and for the number of (equivalence classes
of) permutation actions of any given poly-Σ group. 相似文献
11.
Recent work by a number of people has shown that complex reection groups give rise to many representation-theoretic structures
(e.g., generic degrees and families of characters), as though they were Weyl groups of algebraic groups. Conjecturally, these
structures are actually describing the representation theory of as-yet undescribed objects called spetses, of which reductive algebraic groups ought to be a special case.
In this paper we carry out the Lusztig–Shoji algorithm for calculating Green functions for the dihedral groups. With a suitable
set-up, the output of this algorithm turns out to satisfy all the integrality and positivity conditions that hold in the Weyl
group case, so we may think of it as describing the geometry of the “unipotent variety” associated to a spets. From this,
we determine the possible “Springer correspondences,” and we show that, as is true for algebraic groups, each special piece
is rationally smooth, as is the full unipotent variety.
DOI: .
Supported by NSF grant DMS-0500873. 相似文献
12.
The class of cellularly stratified algebras is defined and shown to include large classes of diagram algebras. While the definition
is in combinatorial terms, by adding extra structure to Graham and Lehrer’s definition of cellular algebras, various structural
properties are established in terms of exact functors and stratifications of derived categories. The stratifications relate
‘large’ algebras such as Brauer algebras to ‘smaller’ ones such as group algebras of symmetric groups. Among the applications
are relative equivalences of categories extending those found by Hemmer and Nakano and by Hartmann and Paget, as well as identities
between decomposition numbers and cohomology groups of ‘large’ and ‘small’ algebras. 相似文献
13.
N. S. Markaryan 《Mathematical Notes》1996,59(6):611-617
In the paper, the homology of the braid groups with twisted coefficients and the homology of commutator subgroups of the braid
groups are calculated. The main tool is the multiplicative structure on the homology induced by the “addition” of braid groups.
Translated fromMatematicheskie Zametki, Vol. 59, No. 6, pp. 846–854, June, 1996.
This research was partially supported by the International Science Foundation under grant MQO000. 相似文献
14.
Dmitrii Zinoviev 《Israel Journal of Mathematics》1998,106(1):29-77
We relate the “Fourier” orbital integrals of corresponding spherical functions on thep-adic groups SO(5) and PGL(2). The correspondence is defined by a “lifting” of representations of these groups. This is a
local “fundamental lemma” needed to compare the geometric sides of the global Fourier summation formulae (or relative trace
formulae) on these two groups. This comparison leads to conclusions about a well known lifting of representations from PGL(2)
to PGSp(4). This lifting produces counter examples to the Ramanujan conjecture. 相似文献
15.
An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata.
We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative
groups, nilpotent groups of class n ≥ 2) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative
groups, nilpotent groups of class n ≥ 2) is neither a Σ21-set nor a Π21-set. 相似文献
16.
Assaf Libman 《Mathematische Zeitschrift》2007,255(3):515-548
We give a new proof of the Minami–Webb formula for classifying spaces of finite groups by exploiting Symonds’s resolution
of Webb’s conjecture. The methods are applicable to obtain a stable decomposition of Minami’s type for the classifying spaces
of the three exotic p-local finite groups which were introduced by Ruiz and Viruel at the prime 7. We obtain a similar decomposition for the classifying
spaces of a family of exotic p-local finite groups which were constructed by Broto, Levi and Oliver.
The author was supported by the Nuffield Foundation Grant NAL/00735/G. 相似文献
17.
Let B be a class of groups A which are soluble, equationally Noetherian, and have a central series A = A1 ⩾ A2 ⩾ … An ⩾ … such that ⋂An = 1 and all factors An/An+1 are torsion-free groups; D is a direct product of finitely many cyclic groups of infinite or prime orders. We prove that
the wreath product D ≀ A is an equationally Noetherian group. As a consequence we show that free soluble groups of arbitrary
derived lengths and ranks are equationally Noetherian.
Supported by RFBR grant No. 05-01-00292.
__________
Translated from Algebra i Logika, Vol. 46, No. 1, pp. 46–59, January–February, 2007. 相似文献
18.
We show that in the constructible universe, the two usual definitions of Butler groups are equivalent for groups of arbitrarily
large power. We also prove that Bext2(G, T) vanishes for every torsion-free groupG and torsion groupT. Furthermore, balanced subgroups of completely decomposable groups are Butler groups. These results have been known, under
CH, only for groups of cardinalities ≤ ℵω.
Partial support by NSF is gratefully acknowledged.
Partially supported by U.S.-Israel Binational Science Foundation. 相似文献
19.
An Abelian group A is called correct if for any Abelian group B isomorphisms A ≅ B′ and B ≅ A′, where A′ and B′ are subgroups of the groups A and B, respectively, imply the isomorphism A ≅ B. We say that a group A is determined by its subgroups (its proper subgroups) if for any group B the existence of a bijection between the sets of all subgroups (all proper subgroups) of groups A and B such that corresponding subgroups are isomorphic implies A ≅ B. In this paper, connections between the correctness of Abelian groups and their determinability by their subgroups (their
proper subgroups) are established. Certain criteria of determinability of direct sums of cyclic groups by their subgroups
and their proper subgroups, as well as a criterion of correctness of such groups, are obtained.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 21–36, 2003. 相似文献
20.
The notions Hodge–Newton decomposition and Hodge–Newton filtration for F-crystals are due to Katz and generalize Messing’s result on the existence of the local-étale filtration for p-divisible groups. Recently, some of Katz’s classical results have been generalized by Kottwitz to the context of F-crystals with additional structures and by Moonen to μ-ordinary p-divisible groups. In this paper, we discuss further generalizations to the situation of crystals in characteristic p and of p-divisible groups with additional structure by endomorphisms. 相似文献