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1.
We compute maximal orders of unipotent Abelian subgroups, estimate p-ranks, and describe the structure of Thompson subgroups of maximal unipotent subgroups of finite exceptional groups of Lie type.  相似文献   

2.
3.
Let be ak-net of ordern with line-point incidence matrixN and letA be the adjacency matrix of its collinearity graph. In this paper we study thep-ranks (that is, the rank over ) of the matrixA+kl withp a prime dividingn. SinceA+kI=N T N thesep-ranks are closely related to thep-ranks ofN. Using results of Moorhouse on thep-ranks ofN, we can determiner p (A+kI) if is a 3-net (latin square) or a desarguesian net of prime order. On the other hand we show how results for thep-ranks ofA+kI can be used to get results for thep-ranks ofN, especially in connection with the Moorhouse conjecture. Finally we generalize the result of Moorhouse on thep-rank ofN for desarguesian nets of orderp a bit to special subnets of the desarguesian affine plane of orderp e .The author is financially supported by the Cooperation Centre Tilburg and Eindhoven Universities.  相似文献   

4.
《代数通讯》2013,41(5):2141-2160
Abstract

Let A be a Noetherian ring graded by a finitely generated Abelian group G. It is shown that a Chow group A ?(A) of A is determined by cycles and a rational equivalence with respect to certain G-graded ideals of A. In particular, A ?(A) is isomorphic to the equivariant Chow group of A if G is torsion free.  相似文献   

5.
In this note we study finite p-groups G = AB admitting a factorization by an Abelian subgroup A and a subgroup B. As a consequence of our results we prove that if B contains an Abelian subgroup of index p n−1 then G has derived length at most 2n.  相似文献   

6.
Peter Danchev 《代数通讯》2013,41(3):933-947
We study the existence of several classes 𝒦 of Abelian p-groups, p a fixed prime, which possess the following property: A ∈ 𝒦?A/F ∈ 𝒦, whenever F is a finite subgroup of the Abelian p-group A.  相似文献   

7.
We study into the relationship between constructivizations of an associative commutative ring K with unity and constructivizations of matrix groups GL n(K) (general), SL n(K) (special), and UT n(K) (unitriangular) over K. It is proved that for n 3, a corresponding group is constructible iff so is K. We also look at constructivizations of ordered groups. It turns out that a torsion-free constructible Abelian group is orderly constructible. It is stated that the unitriangular matrix group UT n(K) over an orderly constructible commutative associative ring K is itself orderly constructible. A similar statement holds also for finitely generated nilpotent groups, and countable free nilpotent groups.  相似文献   

8.
Let be a distance-regular graph with adjacency matrix A. Let I be the identity matrix and J the all-1 matrix. Let p be a prime. We study the p-rank of the matrices A + bJcI for integral b, c and the p-rank of corresponding matrices of graphs cospectral with .Using the minimal polynomial of A and the theory of Smith normal forms we first determine which p-ranks of A follow directly from the spectrum and which, in general, do not. For the p-ranks that are not determined by the spectrum (the so-called relevant p-ranks) of A the actual structure of the graph can play a rôle, which means that these p-ranks can be used to distinguish between cospectral graphs.We study the relevant p-ranks for some classes of distance-regular graphs and try to characterize distance-regular graphs by their spectrum and some relevant p-rank.  相似文献   

9.
Let C be an Abelian group. An Abelian group A in some class of Abelian groups is said to be C H-definable in the class if, for any group B\in , it follows from the existence of an isomorphism Hom(C,A) Hom(C,B) that there is an isomorphism A B. If every group in is C H-definable in , then the class is called an C H-class. In the paper, conditions are studied under which a class of completely decomposable torsion-free Abelian groups is a C H-class, where C is a completely decomposable torsion-free Abelian group.  相似文献   

10.
For a finite group G, let Cent(G) denote the set of centralizers of single elements of G and #Cent(G) = |Cent(G)|. G is called an n-centralizer group if #Cent(G) = n, and a primitive n-centralizer group if #Cent(G) = #Cent(G/Z(G)) = n. In this paper, we compute #Cent(G) for some finite groups G and prove that, for any positive integer n 2, 3, there exists a finite group G with #Cent(G) = n, which is a question raised by Belcastro and Sherman [2]. We investigate the structure of finite groups G with #Cent(G) = 6 and prove that, if G is a primitive 6-centralizer group, then G/Z(G) A4, the alternating group on four letters. Also, we prove that, if G/Z(G) A4, then #Cent(G) = 6 or 8, and construct a group G with G/Z(G) A4 and #Cent(G) = 8.This research was in part supported by a grant from IPM.2000 Mathematics Subject Classification: 20D99, 20E07  相似文献   

11.
A. Kirk 《代数通讯》2013,41(9):3357-3386
Tararin has shown that a non-Abelian group G admits a nonzero finite number of distinct right-orders if and only if G is equipped with a Tararin-type series of some length n. Further, a group which has a Tararin-type series of length n admits 2 n right-orders. It is known that a group has two right-orders if and only if it is torsionfree Abelian of rank 1. Here we completely classify the groups which admit either four or eight right-orders.  相似文献   

12.
A proper subgroup A of a finite group G is said to be primitive or meet-irreducible if there is a unique subgroup A0 ≤ G such that A is a maximal subgroup of A0. In this case we say that |A0: A| is the small index of A and denote it by |G: A|0. In this article, we study the influence of meet-irreducible subgroups and their small indexes on the structure of G. In particular, we prove that a finite group G is supersoluble if and only if |G: A|0 = |G: B|0 for any two meet-irreducible subgroups A and B of G with AG = BG.  相似文献   

13.
Claude Marion 《代数通讯》2013,41(3):926-954
Let p1, p2, p3 be primes. This is the final paper in a series of three on the (p1, p2, p3)-generation of the finite projective special unitary and linear groups PSU 3(pn), PSL 3(pn), where we say a noncyclic group is (p1, p2, p3)-generated if it is a homomorphic image of the triangle group Tp1, p2, p3 . This article is concerned with the case where p1 = 2 and p2 ≠ p3. We determine for any primes p2 ≠ p3 the prime powers pn such that PSU 3(pn) (respectively, PSL 3(pn)) is a quotient of T = T2, p2, p3 . We also derive the limit of the probability that a randomly chosen homomorphism in Hom(T, PSU 3(pn)) (respectively, Hom(T, PSL 3(pn))) is surjective as pn tends to infinity.  相似文献   

14.
In this paper,we shall mainly study the p-solvable finite group in terms of p-local rank,and a group theoretic characterization will be given of finite p-solvabel groups with p-local rank two.Theorem A Let G be a finite p-solvable group with p-local rank plr(G)=2 and Op(G)=1.If P is a Sylow p-subgrounp of G,then P has a normal subgroup Q such that P/Q is cyclic or a generalized quaternion 2-group and the p-rank of Q is at most two.Theorem B Let G be a finite p-solvable group with Op(G)=1.Then the p-length lp(G)≤plr(G);if in addition plr(G)=lp (G) and p≥5 is odd,then plr(G)=0 or 1.  相似文献   

15.
LetA n, n≥0, be a variety of all Abelian groups whose exponental divides n. We establish a criterion of being primitive for varieties of the formA m A n, and study into the question of inducing primitive systems of elements in free groups of these. The results obtained give a solution to the problem by Bachmuth and Mochizuki concerning the tame range of varietiesA m A n for the case where m is freed of squares, and lend support to the conjecture by Bryant and Gupta as to inducing primitive, systems for varieties likeA pnA. This author’s part is supported by RFFR grant No. 99-01-00567. Translated fromAlgebra i Logika, Vol. 38, No. 5, pp. 513–530, September–October, 1999.  相似文献   

16.
17.
We call a central Z-extension of a group G weakly universal for an Abelian group A if the correspondence assigning to a homomorphism ZA the corresponding A-extension yields a bijection of extension classes. The main problem discussed in this paper is the existence of central Lie group extensions of a connected Lie group G which is weakly universal for all Abelian Lie groups whose identity components are quotients of vector spaces by discrete subgroups. We call these Abelian groups regular. In the first part of the paper we deal with the corresponding question in the context of topological, Fréchet, and Banach–Lie algebras, and in the second part we turn to the groups. Here we start with a discussion of the weak universality for discrete Abelian groups and then turn to regular Lie groups A. The main results are a Recognition and a Characterization Theorem for weakly universal central extensions.  相似文献   

18.
Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a result of W. May argued when G is p-local Warfield Abelian and published in Proc. Amer. Math. Soc. (1988).  相似文献   

19.
《Quaestiones Mathematicae》2013,36(1):103-120
Abstract

We characterize Abelian groups with a minimal generating set: Let τ A denote the maximal torsion subgroup of A. An infinitely generated Abelian group A of cardinality κ has a minimal generating set iff at least one of the following conditions is satisfied:
  1. dim(A/pA) = dim(A/qA) = κ for at least two different primes p, q.

  2. dim(t A/pt A) = κ for some prime number p.

  3. Σ{dim(A/(pA + B)) dim(A/(pA + B)) < κ} = κ for every finitely generated subgroup B of A.

Moreover, if the group A is uncountable, property (3) can be simplified to (3') Σ{dim(A/pA) dim(A/pA) < κ} = κ, and if the cardinality of the group A has uncountable cofinality, then A has a minimal generating set iff any of properties (1) and (2) is satisfied.  相似文献   

20.
It is well known that there is a close connection between tame kernels and ideal class groups of number fields. However, the latter is a very difficult subject in number theory. In this paper, we prove some results connecting the p^n-rank of the tame kernel of a cyclic cubic field F with the p^n-rank of the coinvariants of μp^n×CI(δE,T) under the action of the Galois group, where E = F(ζp^n ) and T is the finite set of primes of E consisting of the infinite primes and the finite primes dividing p. In particular, if F is a cyclic cubic field with only one ramified prime and p = 3, n = 2, we apply the results of the tame kernels to prove some results of the ideal class groups of E, the maximal real subfield of E and F(ζ3).  相似文献   

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