共查询到20条相似文献,搜索用时 35 毫秒
1.
Carlo Toffalori 《Mathematical Logic Quarterly》1996,42(1):433-445
We extend the analysis of the decision problem for modules over a group ring ?[G] to the case when G is a cyclic group of squarefree order. We show that separated ?[G]-modules have a decidable theory, and we discuss the model theoretic role of these modules within the class of all ?[G]-modules. The paper includes a short analysis of the decision problem for the theories of (finitely generated) modules over ?[ζm], where m is a positive integer and ζm is a primitive mth root of 1. Mathematics Subject Classification: 03C60, 03B25. 相似文献
2.
Francis Oger 《Archive for Mathematical Logic》2001,40(7):515-521
We show that, for each finite group G, there exists an axiomatization of the class of abelian-by-G groups with a single sentence. In the proof, we use the definability of the subgroups M
n
in an abelian-by-finite group M, and the Auslander-Reiten sequences for modules over an Artin algebra.
Received: 15 March 1996 / Published online: 18 July 2001 相似文献
3.
Alexei Myasnikov 《Journal of Pure and Applied Algebra》2011,215(11):2789-2796
We call a group Galgorithmically finite if no algorithm can produce an infinite set of pairwise distinct elements of G. We construct examples of recursively presented infinite algorithmically finite groups and study their properties. For instance, we show that the Equality Problem is decidable in our groups only on strongly (exponentially) negligible sets of inputs. 相似文献
4.
Thierry Coulbois 《Archive for Mathematical Logic》2001,40(7):523-524
F. Oger proved that if A is a finite group, then the class of groups which are abelian-by-A can be axiomatized by a single first order sentence. It is established here that, in Oger's result, the word abelian cannot
be replaced by group.
Received: 15 March 1996 / Published online: 18 July 2001 相似文献
5.
John R. Klein 《Mathematische Annalen》2001,319(3):421-456
To a topological group G, we assign a naive G-spectrum , called the dualizing spectrum of G. When the classifying space BG is finitely dominated, we show that detects Poincaré duality in the sense that BG is a Poincaré duality space if and only if is a homotopy finite spectrum. Secondly, we show that the dualizing spectrum behaves multiplicatively on certain topological
group extensions. In proving these results we introduce a new tool: a norm map which is defined for any G and for any naive G-spectrum E. Applications of the dualizing spectrum come in two flavors: (i) applications in the theory of Poincaré duality spaces, and
(ii) applications in the theory of group cohomology. On the Poincaré duality space side, we derive a homotopy theoretic solution
to a problem posed by Wall which says that in a fibration sequence of fini the total space satisfies Poincaré duality if and
only if the base and fiber do. The dualizing spectrum can also be used to give an entirely homotopy theoretic construction
of the Spivak fibration of a finitely dominated Poincaré duality space. We also include a new proof of Browder's theorem that
every finite H-space satisfies Poincaré duality. In connection with group cohomology, we show how to define a variant of Farrell-Tate cohomology
for any topological or discrete group G, with coefficients in any naive equivariant cohomology theory E. When E is connective, and when G admits a subgroup H of finite index such that BH is finitely dominated, we show that this cohomology coincides with the ordinary cohomology of G with coefficients in E in degrees greater than the cohomological dimension of H. In an appendix, we identify the homotopy type of for certain kinds of groups. The class includes all compact Lie groups, torsion free arithmetic groups and Bieri-Eckmann
duality groups.
Received July 14, 1999 / Revised May 17, 2000 / Published online February 5, 2001 相似文献
6.
The purpose of this paper is to study the subgroup embedding properties of S-semipermutability, semipermutability, and seminormality.
Here we say H is S-semipermutable (resp. semipermutable) in a group Gif H permutes which each Sylow subgroup (resp. subgroup) of G whose order is relatively prime to that of H. We say H is seminormal in a group G if H is normalized by subgroups of G whose order is relatively prime to that of H. In particular, we establish that a seminormal p-subgroup is subnormal. We also establish that the solvable groups in which S-permutability is a transitive relation are precisely
the groups in which the subnormal subgroups are all S-semipermutable. Local characterizations of this result are also established. 相似文献
7.
In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ?[G] satisfies the multiplicative Jordan decomposition (MJD). In the nonabelian case, we show that ?[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27. 相似文献
8.
Abderezak Ould Houcine 《代数通讯》2013,41(10):3719-3723
We prove that an abelian group G is a countable direct sum of finite cyclic groups if and only if there exists a consistent existential theory Γ of abelian groups such that G is embeddable in every model of Γ. 相似文献
9.
Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.
M. Otero was Partially supported by GEOR MTM2005-02568 and Grupos UCM 910444. 相似文献
10.
11.
A group G is generically trivial if and only if, for all prime numbers p the localization of G with respect to p is trivial. Taking off from a theorem of Casacuberta and Castellet , we prove that a virtually nilpotent group E is generically trivial if and only if E is perfect. Inspired by this result, we introduce the concept of almost generically trivial groups. Those are groups G such that, for only finitely many primes p the localization of G with respect to p is not trivial. We prove that a virtually nilpotent group E with finitely generated abelianization is almost generically trivial if and only if the abelianization of E is finite. 相似文献
12.
Ilya Kapovich Alexei Myasnikov Paul Schupp Vladimir Shpilrain 《Advances in Mathematics》2005,190(2):91-359
We investigate the average-case complexity of decision problems for finitely generated groups, in particular, the word and membership problems. Using our recent results on “generic-case complexity”, we show that if a finitely generated group G has word problem solvable in subexponential time and has a subgroup of finite index which possesses a non-elementary word-hyperbolic quotient group, then the average-case complexity of the word problem of G is linear time, uniformly with respect to the collection of all length-invariant measures on G. This results applies to many of the groups usually studied in geometric group theory: for example, all braid groups Bn, all groups of hyperbolic knots, many Coxeter groups and all Artin groups of extra-large type. 相似文献
13.
Let G be the direct sum of the noncyclic groupof order four and a cyclic groupwhoseorderisthe power pn of some prime p. We show that ℤ2 G‐lattices have a decidable theory when the cyclotomic polynomia (x) is irreducible modulo 2ℤ for every j ≤ n. More generally we discuss the decision problem for ℤ2 G‐lattices when G is a finite group whose Sylow 2‐subgroups are isomorphic to the noncyclic group of order four. 相似文献
14.
Let G be a group. In this note we define conjugate closed groups, which are briefly called CC — Groups. These groups form a proper subclass of T — Groups. We prove that if G = Z(G) × H, then G is conjugate closed if and only if H is conjugate closed. We also show that a finite group G is semisimple, conjugate
closed and perfect if and only if it is a direct product of non-abelian and simple groups. 相似文献
15.
Recall that a finite group G satisfies the one-prime hypothesis if the greatest common divisor for any pair of distinct degrees in cd(G) is either 1 or a prime. In this paper, we classify the nonsolvable groups that satisfy the one-prime hypothesis. As a consequence
of our classification, we show that if G is a nonsolvable group satisfying the one-prime hypothesis, then |cd(G)| ≤ 8, and hence, if G is any group satisfying the one-prime hypothesis, then |cd(G)| ≤ 9.
Presented by Don Passman. 相似文献
16.
Mark L. Lewis 《代数通讯》2013,41(4):1273-1292
A finite group G is odd-square-free if no irreducible complex character of G has degree divisible by the square of an odd prime. We determine all odd-square-free groups G satisfying S ≤ G ≤ Aut(S) for a finite simple group S. More generally, we show that if G is any nonsolvable odd-square-free group, then G has at most two nonabelian chief factors and these must be simple odd-square-free groups. If the alternating group A 7 is involved in G, the structure of G can be further restricted. 相似文献
17.
A finite group G is called rational if all its irreducible complex characters are rational valued. In this paper, we show that if G is a direct product of finitely many rational Frobenius groups then every rationally represented character of G is a generalized permutation character. Also we show that the same assertion holds when G is a solvable rational group with a Sylow 2-subgroup isomorphic to the dihedral group of order 8 and an abelian normal Sylow 3-subgroup. 相似文献
18.
Jon Gonz��lez-S��nchez 《Archiv der Mathematik》2010,94(3):201-205
Let G be a finite group, p a fixed prime and P a Sylow p-subgroup of G. In this short note we prove that if p is odd, then G is p-nilpotent if and only if P controls fusion of cyclic groups of order p. For the case p = 2, we show that G is p-nilpotent if and only if P controls fusion of cyclic groups of order 2 and 4. 相似文献
19.
In [6] squarelike groups were defined to be those groups G universally equivalent to their direct squares G × G. In that paper it was shown that G is squarelike if and only if G is
universally equivalent to a discriminating group in the sense of [3]. Further it was shown that the
class of squarelike groups is first-order axiomatizable while the class of discriminating groups is
not. In this paper, we prove that the class of squarelike groups is the least axiomatic class containing
the discriminating groups.Received: 18 August 2003 相似文献
20.
Ján Jakubík 《Czechoslovak Mathematical Journal》2000,50(3):587-602
We denote by F
a the class of all abelian lattice ordered groups H such that each disjoint subset of H is finite. In this paper we prove that if G F
a, then the cut completion of G coincides with the Dedekind completion of G. 相似文献