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1.
考察元素的阶如何影响有限群的结构是群论中的一个重要课题.本文研究存在一个正规子群N,N外的元素都是素数阶元的有阶群.主要利用熟知的Thompson的一个定理,获得了这样的有限群. 相似文献
2.
本文研究了L—Fuzzy群的同态和同构,给出了它们的一些性质,并把群论中的同态定理和同构定理推广到L—Fuzzy群上 相似文献
3.
用阶刻划单群及有关课题 总被引:4,自引:0,他引:4
“群的阶”与“元的阶”是群论的两个最基本的概念,但它们在群的研究中起着重要的作用。 1902年W.Burnside提出如下著名的问题:若群G为有限生成,G中元的阶均为有限,G的阶是否有限?虽然Burnside的问题已由Golod给出了否定的答案,但它突出了“元的阶”在群的结构中的作用。 相似文献
4.
群类理论是在有限可解群研究工作的基础上发展起来的,但近年来对有限群论的许多方面都起到越来越大的作用.在考察群类性质时,注意到一个Fitting类(?)在可解群G中的(?)内射子具有Sylow子群所具有的某些性质,并且关于Sylow定理中(Sy13),证明了对于群的本原子群,成立更强的结论. 相似文献
5.
通过计算群中的对合数,本文刻画了以下两类有限群:特征标表中有一行至多有两个有理值的有限群;特征标表中有一列至多有两个实数值的有限群. 相似文献
6.
群的遗传根性和强半单根性 总被引:1,自引:0,他引:1
本文利用群的根性的性质,解决了Szasz在环的根性理论中提出的公开问题在群论中的对应问题.同时我们研究了群的遗传根性和强半单根性的一些性质,并介绍了群的根类的交运算和并运算,由此得到了一些很好的结果. 相似文献
7.
有两个对偶的问题如下:问题Ⅰ:将满足下述条件的有限群G分类:G的特征标表中,除一行外其余各行最多有一个零.问题Ⅱ:将满足下述条件的有限群G分类:G的特征标表中,除一列外其余各列最多有一个零.在这篇文章中,我们对于有限可解群解答上述两个问题,并确定和这两个问题密切相关的一类有限可解群的结构(这类可解群在本文中称之为可解φ-群).附带我们还完全回答了[4]中的问题1,并说明[6,定理]的条件可以极大地减弱. 相似文献
8.
本文研究有限群元素共轭类的平均长度问题.利用初等群论方法和有限群特征标理论,在共轭类平均长度为某一定数时,获得了对有限群结构的刻划,且对有限群数量性质的研究是有意义的. 相似文献
9.
群环理论将群论和环论有机地结合了起来,是代数学中的重要分支之一,其中增广理想和增广商群是群环理论中的一个经典课题.设G有限群,分别记的Burnside环及其增广理想为Ω(G)和Δ(G).本文对任意正整数n,具体构造了Δ~n(I_p)作为自由交换群的一组基,并确定了商群Δ~n(I_p)/Δ~(n+1)(I_p)的结构,其中I_p=〈a,b|a~(p~2)=b~p=1,b~(-1)ab=a~(p+1)〉,p为奇素数. 相似文献
10.
11.
For finite rank free abelian groups with the standard presentation, the averaged Dehn function is proved to be subquadratic. 相似文献
12.
We introduce two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function)
for infinite group presentations and prove the fundamental equivalence between the solvability of the word problem for a group
presentation defined by a decidable set of defining words and the property of being computable for one of the newly introduced
functions (this equivalence fails for the standard Dehn function). Elaborating on this equivalence and making use of this
function, we obtain a characterization of finitely generated groups for which the word problem can be solved in nondeterministic
polynomial time.
We also give upper bounds for these functions, as well as for the standard Dehn function, for two well-known periodic groups.
In particular, we prove that the (standard) Dehn function of a 2-group Γ of intermediate growth, defined by a system of defining
relators due to Lysenok, is bounded from above by C1x2 log2 x, where C1 > 1 is a constant. We also show that the (standard) Dehn function of a free m-generator Burnside group B(m, n) of exponent n ≥ 248, where n is either odd or divisible by 29, defined by a minimal system of defining relators, is bounded from above by the subquadratic function x19/12.
Received: September 2007, Revision: March 2008, Accepted: March 2008 相似文献
13.
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
14.
We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function
n2log n. Some of these groups have undecidable conjugacy problem. Our groups are multiple HNN extensions of free groups. We show
that n2log n is the smallest Dehn function of a multiple HNN extension of a free group with undecidable conjugacy problem.
Both authors were supported in part by the NSF grants DMS 0245600 and DMS 0455881. In addition, the research of the first
author was supported in part by the Russian Fund for Basic Research 05-01-00895, the research of the second author was supported
in part by the NSF grant DMS 9978802 and the US-Israeli BSF grant 1999298.
Received: February 2005; Revision: September 2005; Accepted: September 2005 相似文献
15.
A left-cancellative automatic monoid having directed fellow traveller property is finitely presented, and the first order
Dehn functions of such automatic monoids are bounded above by a quadratic function. These results coincide with those of automatic
groups.
The research of X. Wang was partially supported by China National Science Funds (No:10771077 and 10671114). 相似文献
16.
A Dehn twist automorphism of a group G is an automorphism which can be given (as specified below) in terms of a graph-of-groups decomposition of G with infinite cyclic edge groups. The classic example is that of an automorphism of the fundamental group of a surface which
is induced by a Dehn twist homeomorphism of the surface. For , a non-abelian free group of finite rank n, a normal form for Dehn twist is developed, and it is shown that this can be used to solve the conjugacy problem for Dehn
twist automorphisms of .
Received: February 12, 1996. 相似文献
17.
Moritz GRUBER 《Frontiers of Mathematics in China》2016,11(5):1239-1258
This survey gives an overview of the isoperimetric properties of nilpotent groups and Lie groups. It discusses results for Dehn functions and filling functions as well as the techniques used to retrieve them. The content reaches from long standing results up to the most recent development. 相似文献
18.
We extend the range of observed behaviour among length functionsof optimal asynchronously automatic structures. We do so bymeans of a construction that yields asynchronously automaticgroups with finite aspherical presentations where the Dehn functionof the group is polynomial of arbitrary degree. Many of thesegroups can be embedded in the automorphism group of a free group.Moreover, the fact that the groups have aspherical presentationsmakes them useful tools in the search to determine the spectrumof exponents for second order Dehn functions. We contributeto this search by giving the first exact calculations of groupswith quadratic and superquadratic exponents. 2000 Mathematical Subject Classification: 20F06, 20F65, 20F69. 相似文献
19.
Naoyuki Monden 《Topology and its Applications》2012,159(4):1085-1091
We give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating curve on an oriented closed surface of genus 2 are not equal to each other. 相似文献
20.
Chaohui ZHANG 《数学年刊B辑(英文版)》2014,35(1):79-92
Let S be a hyperbolic Riemann surface with a finite area.Let G be the covering group of S acting on the hyperbolic plane H.In this paper,the author studies some algebraic relations in the mapping class group of(?) for(?) — S\{a point}.The author shows that the only possible relations between products of two Dehn twists and products of mapping classes determined by two parabolic elements of G are the reduced lantern relations.As a consequence,a partial solution to a problem posed by J.D.McCarthy is obtained. 相似文献