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A class of loops categorically isomorphic to uniquely 2-divisible Bruck loops
T-loops Bruck loops uniquely 2-divisible power-associativity
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2012/6/26
We define a new variety of loops we call $\Gamma$-loops. After showing $\Gamma$-loops are power associative, our main goal will be showing a categorical isomorphism between uniquely 2-divisible Bruck ...
Word maps with small image in simple groups
Word maps with small image simple groups Group Theory
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2012/6/25
We construct non-power words which have small image in SL(2; 22n) for each n. In particular, the corresponding word maps are non-surjective. We also use this to construct word maps whose values are pr...
Abels's groups revisited
Abels's groups Group Theory Geometric Topology
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2012/6/21
The homological finiteness length of a group G is the maximal length (counting from 0) of a partial resolution by finitely generated projective modules of the trivial ZG-module Z. It is closely relate...
Brown's criterion in Bredon homology
Brown's criterion Bredon homology Group Theory
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2012/6/21
We translate Brown's criterion for homological finiteness properties to the setting of Bredon homology.
Characterizing sequences for precompact group topologies
precompact group topology T -sequence TB-sequence characterizing sequence characterized subgroup Bembedded subgroup finest precompact extension
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2012/6/19
A precompact group topology $\tau$ on an abelian group $G$ is called {\em single sequence characterized} (for short, {\em ss-characterized}) if there is a sequence $\mathbf{u}= (u_n)$ in $G$ such that...
Cannon-Thurston maps do not always exist
hyperbolic group Cannon–Thurston map Group Theory
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2012/6/19
We construct an example of a hyperbolic group with a hyperbolic subgroup for which the Cannon-Thurston map does not exist. That is, inclusion does not induce a map of the boundaries.
Golod-Shafarevich groups: a survey
Golod-Shafarevich groups subgroup growth class field tower problem Burnside problem
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2012/6/19
In this paper we survey the main results about Golod-Shafarevich groups and their applications in algebra, number theory and topology.
Recognising the small Ree groups in their natural representations
the small Ree groups their natural representations Group Theory
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2012/6/15
We present Las Vegas algorithms for constructive recognition and constructive membership testing of the Ree groups 2G_2(q) = Ree(q), where q = 3^{2m + 1} for some m > 0, in their natural representatio...
Cross-wired lamplighter groups
Cross-wired lamplighter groups Group Theory
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2012/6/18
We give a necessary and sufficient condition for a locally compact group to be isomorphic to a closed cocompact subgroup in the isometry group of a Diestel-Leader graph. As a consequence of this condi...
The first $L^2$-Betti number and approximation in arbitrary characteristic
First L2-Betti number approximation in prime characteristic Group Theory
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2012/6/19
Let G be a finitely generated group and (G_i) a descending chain of finite index normal subgroups of G. Given a field K, we consider the sequence b_1(G_i;K)/[G:G_i] of normalized first Betti numbers o...
Epimorphisms from 2-bridge link groups onto Heckoid groups (II)
Epimorphisms 2-bridge link groups Group Theory
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2012/6/18
We describe all upper-meridian-pair-preserving epimorphisms from 2-bridge link groups onto even Heckoid groups.
On partially conjugate-permutable subgroups of finite groups
conjugate-permutable subgroups of finite groups Group Theory
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2012/6/12
Let $R$ be a subset of a group $G$. We call a subgroup $H$ of $G$ the $R$-conjugate-permutable subgroup of $G$, if $HH^{x}=H^{x}H$ for all $x\in R$. This concept is a generalization of conjugate-permu...
On the Quiver Presentation of the Descent Algebra of the Symmetric Group
Descent algebra symmetric group quiver presentation
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2012/6/15
We describe a presentation for the descent algebra of the symmetric group $\sym{n}$ as a quiver with relations. This presentation arises from a new construction of the descent algebra as a homomorphic...
Sylow子群的极大子群s*-置换嵌入的有限群
s*-置换嵌入 s-置换 p幂零 超可解
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2012/11/13
利用Sylow子群的极大子群的s*-置换嵌入性研究有限群的p幂零性和超可解性, 并给出了一个群属于给定的饱和群系的新的判别准则。
Homological and homotopical Dehn functions are different
Homological and homotopical Dehn functions Group Theory
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2012/5/24
The homological and homotopical Dehn functions are different ways of measuring the difficulty of filling a closed curve inside a group or a space. The homological Dehn function measures fillings of cy...