共查询到20条相似文献,搜索用时 0 毫秒
1.
James P. Cossey 《代数通讯》2018,46(8):3356-3364
2.
Antonio Tortora 《代数通讯》2013,41(2):431-438
For any integer n ≠ 0,1, a group G is said to be “n-Bell” if it satisfies the identity [x n ,y] = [x,y n ]. It is known that if G is an n-Bell group, then the factor group G/Z 2(G) has finite exponent dividing 12n 5(n ? 1)5. In this article we show that this bound can be improved. Moreover, we prove that every n-Bell group is n-nilpotent; consequently, using results of Baer on finite n-nilpotent groups, we give the structure of locally finite n-Bell groups. Finally, we are concerned with locally graded n-Bell groups for special values of n. 相似文献
3.
Bijan Taeri 《代数通讯》2013,41(3):894-922
Let n be an integer greater than 1. A group G is said to be “ n-rewritable” whenever for every n elements x 1,…,x n of G, there exist distinct permutations τ, σ on the set {1,2,…, n} such that x τ(1) ··· x τ(n) = x σ (1) ··· x σ (n). In this article, we complete the classification of 3-rewritable finite nilpotent groups and prove that a finite nilpotent group G is 3-rewritable if and only if G has an abelian subgroup of index 2 or the derived subgroup has order < 6. 相似文献
5.
I. Lizasoain 《数学学报(英文版)》2010,26(3):405-418
Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups (G-groups). In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible. 相似文献
6.
In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G p |<∞ (of course, it contains G = G p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞. 相似文献
7.
《代数通讯》2013,41(5):1417-1425
ABSTRACT Let n be an integer greater than 1. A group G is said to be n-rewritable (or a Qn-group) if for every n elements x1, x2,…,xn in G there exist distinct permutations σ and τ in Sn such that xσ(1)xσ (2) ??? xσ(n) = xτ(1)xτ(2) ??? xτ(n). In this paper, we characterize all 3-rewritable nilpotent 2-groups of class 2. Also we have found a bound for the nilpotency class of certain nilpotent 3-rewritable groups, and have shown that 3-rewritable groups satisfy a certain law. 相似文献
8.
A. Jaikin-Zapirain 《Mathematische Zeitschrift》2006,253(2):333-345
In this paper we prove that if R is a commutative Noetherian local pro-p domain of characteristic 0, then every finitely generated R-standard group is linear.
This work has been partially supported by the FEDER, the MEC Grant MTM2004-04665 and the Ramón y Cajal Program. 相似文献
9.
A Garside group is a group admitting a finite lattice generating set
. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice
, and there is a simple sufficient condition that implies G is a duality group. The universal covers of these K(π, 1)s enjoy Bestvina's weak nonpositive curvature condition. Under a certain tameness condition, this implies that every
solvable subgroup of G is virtually Abelian. 相似文献
10.
王登银 《数学物理学报(B辑英文版)》2007,27(2):317-328
All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3. 相似文献
11.
主要研究子群置换性质对有限群结构的影响.通过子群的置换性得到一类群,即B 群.B群是全可置换群的扩展,利用全可置换群的p次中心扩张和子群的阶得到B群的一些性质并对B 群的结构进行一些刻画.应用B 群的结构得到有限p (p〉2)群为二元生成的B 群的充要条件. 相似文献
12.
In this note, we modify the“classical”theory of sheaves, in such a way that it includes applications where more than one restriction map between sections is needed. 相似文献
13.
在本文中,我们讨论了带作用群的群系的临界结构,给出了处理允许某些作用群的群的问题的一般方法,作为应用,我们特别给出了关于幂零群及p-幂零群的一些结果。 相似文献
14.
Claude Marion 《代数通讯》2013,41(3):853-925
Let p 1, p 2, p 3 be primes. This is the second article in a series of three on the (p 1, p 2, p 3)-generation of the finite projective special unitary and linear groups PSU3(p n ), PSL3(p n ), where we say a noncyclic group is (p 1, p 2, p 3)-generated if it is a homomorphic image of the triangle group T p 1, p 2, p 3 . This paper is concerned with the case where p 1 = 2 and p 2 = p 3. We determine for any prime p 2 the prime powers p n such that PSU3(p n ) (respectively, PSL3(p n )) is a quotient of T = T 2, p 2, p 2 . We also derive the limit of the probability that a randomly chosen homomorphism in Hom(T, PSU3(p n )) (respectively, Hom(T, PSL3(p n ))) is surjective as p n tends to infinity. 相似文献
15.
Andrea Lucchini 《代数通讯》2020,48(11):4966-4968
16.
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
17.
To solve problems of Gilbert Baumslag and Hanna Neumann, posed in the 1960’s, we construct a nontrivial variety of groups all of whose noncyclic free groups are non-Hopfian. 相似文献
18.
The geometrical properties of cyclically presented groups of Fibonacci type F(r,m, k)and H(r,m,k)are discussed. It is shown that for even rand odd m some infinite family of generalized Fibonacci groups F(r, m, k)cannot be fundamental groups of hyperbolic 3-orbifolds of finite volume. 相似文献
19.
AbstractLet λ(G) be the maximum number of subgroups in an irredundant covering of the finite group G. We prove that if G is a group with λ(G) ≤ 6, then G is supersolvable. We also describe the structure of groups G with λ(G) = 6. Moreover, we show that if G is a group with λ(G)?<?31, then G is solvable. 相似文献
20.
V. Metaftsis 《代数通讯》2013,41(11):3879-3886
We show that if the fundamental group of a finite graph of groups with finitely generated Abelian vertex groups is subgroup separable, then it is linear. 相似文献