Brent Everitt
It is shown that any finitely generated non-elementary Fuchsian group has among its homomorphic images all but finitely many of the alternating groups. This settles in the affirmative a conjecture of Graham Higman.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We consider finite 2-dimensional polyhedral complexes, equipped with piecewise non-positively curved, locally CAT(0) metrics. We give conditions on the complex X that ensure that its fundamental group contains a surface subgroup. Concrete examples covered by our methods include compact quotients of sufficiently thick Fuchsian buildings, where the lattice acts freely and the quotient has at least two vertices.
Finite quotients of Fuchsian groups
本文提出区分不同构有限生成 Fuchsian 群有限商的有效算法，通过共同有限商上的群扩张及特定类型商群构造，并给出区分商阶的显式上界。
Let $\C(Γ)$ be the set of isomorphism classes of the finite groups that are homomorphic images of $Γ$. We investigate the extent to which $\C(Γ)$ determines $Γ$ when $Γ$ is a group of geometric interest. If $Γ_1$ is a lattice in ${\rm{PSL}}(2,\R)$ and $Γ_2$ is a lattice in any connected Lie group, then $\C(Γ_1) = \C(Γ_2)$ implies that $Γ_1$ is isomorphic to $Γ_2$. If $F$ is a free group and $Γ$ is a right-angled Artin group or a residually free group (with one extra condition), then $\C(F)=\C(Γ)$ implies that $F\congΓ$. If $Γ_1<{\rm{PSL}}(2,\Bbb C)$ and $Γ_2< G$ are non-uniform arithmetic latt…
We strengthen Marshall Hall's Theorem to show that free groups are locally extended residually alternating. Let F be any free group of rank at least two, let H be a finitely generated subgroup of infinite index in F and let {g_1,...,g_n} be a finite subset of F-H. Then there is a surjection f from F to a finite alternating group such that f(g_i) is not in f(H) for any i. The techniques of this paper can also provide symmetric quotients.
Let $W$ be a right-angled Coxeter group corresponding to a finite non-discrete graph $\mathcal{G}$ with at least $3$ vertices. Our main theorem says that $\mathcal{G}^c$ is connected if and only if for any infinite index quasiconvex subgroup $H$ of $W$ and any finite subset $\{ γ_1, \ldots , γ_n \} \subset W \setminus H$ there is a surjection $f$ from $W$ to a finite alternating group such that $f (γ_i) \notin f (H)$. A corollary is that a right-angled Artin group splits as a direct product of cyclic groups and groups with many alternating quotients in the above sense. Similarly, finitely gene…
Signatures of alternating group actions with non-zero quotient genus
本文研究了交替群作用于紧黎曼面时商亏格大于0的特征，证明当n>6时所有可能的特征都是实际存在，n=5或6时仅[1;2]或[1;3]失效，并证明非阿贝尔单群的所有商亏格大于1的特征都是实际存在。
Tame automorphism groups of polynomial rings with property (T) and infinitely many alternating group quotients
本文构造了具有性质（T）且有无穷多个交错群商的新群族，包括由驯顺自同构生成的多项式环自同构子群，并由此得到显式的 Gromov 双曲群表示及交错群的度为4的扩张器 Cayley 图无限族。
We prove that the smallest non-trivial quotients of the commutator subgroups of the braid groups are the alternating groups, proving a conjecture of Chudnovsky-Kordek-Li-Partin. Furthermore, we show that any minimal quotient map is the standard projection, composed with an automorphism of the alternating group.
Cocompact Fuchsian groups with a modular embedding
本文研究了具有模嵌入的紧致非算术弗希斯曼群，证明了复超曲面中完全测地曲线的模嵌入性质及算术性结论。
Essential quotients of the cohomology of products of symmetric and alternating groups
本文计算对称群与交错群乘积的模二上同调关于可忽略元素的商，回答Serre提出的问题，并基于其近期结果，用于域的上同调不变量研究。
The Yang-Baxter Equation and Characteristic Finite Simple Quotients of the Free Group of Rank $2$
该研究证明无穷多交错群可作为秩2自由群的特征子群核的商群，且存在任意大Lie秩的这类单商群，解决了此前相关论文提出的两个问题。
Thurston and Calegari-Dunfield showed that the fundamental group of some tautly foliated hyperbolic 3-manifold acts on the circle in a distinctive way that the action preserves some structure of S^1, so-called a circle lamination. Indeed, a large class of Kleinian groups acts on the circle preserving a circle lamination. In this paper, we are concerned with the converse problem that a group acting on the circle with at least two invariant circle laminations is Kleinian. We prove that a subgroup of the orientation preserving circle homeomorphism group is a Fuchsian group whose quotient orbifold…
Property (T) and Many Quotients
该研究证明丰富操作子上自由代数的驯自同构群大子群具Kazhdan性质(T)，并推导出存在可满射到交错群大幂次的性质(T)群，拓展了相关群论研究。
A triangle group is denoted by $Δ(p,q,r)$ and has finite presentation $$ Δ(p,q,r)=\langle x,y | x^p=y^q=(xy)^r=1 \rangle .$$ We examine a method for composition of permutation representations of a triangle group $Δ(p,q,r)$ that was used in Everitt's proof of Higman's 1968 conjecture that every Fuchsian group has amongst its homomorphic images all but finitely many alternating groups. We see that some of these compositions must give imprimitive representations, and in particular situations, where the representations being composed are all equivalent copies of an alternating group in the same de…
A Beauville surface (of unmixed type) is a complex algebraic surface which is the quotient of the product of two curves of genus at least 2 by a finite group G acting freely on the product, where G preserves the two curves and their quotients by G are isomorphic to the projective line, ramified over three points. Such a group G is called a Beauville group. We show that if a characteristically simple group G is a cartesian power of a finite simple alternating group, then G is a Beauville group if and only if it has two generators and is not isomorphic to A_5.
In the case where $G=$SL$_{2}(F)$ for a non-archimedean local field $F$ and $Γ$ is a discrete torsion-free cocompact subgroup of $G$, there is a known relationship between the Ihara zeta function for the quotient of the Bruhat-Tits tree of $G$ by the action of $Γ$, and an alternating product of determinants of twisted Poincaré series for parabolic subgroups of the affine Weyl group of $G$. We show how this can be generalised to other split simple algebraic groups of rank two over $F$, and formulate a conjecture about how this might be generalised to groups of higher rank.
Let $P_0(A_n), \widetilde{P}_0(A_n), P_0(\mathcal{T}(A_n))$ and $\mathcal{O}_0(A_n)$ be respectively the proper power graph, the proper quotient power graph, the proper power type graph and the proper order graph of the alternating group $A_n$, for $n\geq 3.$ We determine the number of the components of those graphs. In particular, we prove that the power graph $P(A_n)$ is $2$-connected if and only if the power type graph $P(\mathcal{T}(A_n))$ is $2$-connected, if and only if either $n = 3$ or none of $n, n-1, n-2, \frac{n}{2}$ and ${\frac{n-1}{2}}$ is a prime. We also give some information on…
We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method based on character varieties that can be used to distinguish between the profinite completions of certain groups.
Let PC be the group of bijections from [0, 1[ to itself which are continuous outside a finite set. Let PC be its quotient by the subgroup of finitely supported permutations. We show that the Kapoudjian class of PC vanishes. That is, the quotient map PC $\rightarrow$ PC splits modulo the alternating subgroup of even permutations. This is shown by constructing a nonzero group homomorphism, called signature, from PC to Z 2Z. Then we use this signature to list normal subgroups of every subgroup G of PC which contains S fin and such that G, the projection of G in PC , is simple.
We give new characterizations of sofic groups: -- A group $G$ is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups. -- A group $G$ is sofic if and only if any system of equations solvable in all alternating groups is solvable over $G$. The last characterization allows to express soficity of an existentially closed group by $\forall\exists$-sentences. Keywords: sofic groups, approximations, equations over groups.
A study is carried out of the elementary theory of quotients of symmetric groups in a similar spirit to [Sh:24]. Apart from the trivial and alternating subgroups, the normal subgroups of the full symmetric group S(mu) on an infinite cardinal mu are all of the form S_kappa(mu)= the subgroup consisting of elements whose support has cardinality <kappa for some kappa <= mu^+. A many-sorted structure M_{kappa lambda mu} is defined which, it is shown, encapsulates the first order properties of the group S_lambda (mu)/S_kappa (mu). Specifically, these two structures are (uniformly) bi-interpretable, …
We classify the groups quasi-isometric to a group generated by finite-order elements within the class of one-ended hyperbolic groups which are not Fuchsian and whose JSJ decomposition over two-ended subgroups does not contain rigid vertex groups. To do this, we characterize which JSJ trees of a group in this class admit a cocompact group action with quotient a tree. The conditions are stated in terms of two graphs we associate to the degree refinement of a group in this class. We prove there is a group in this class which is quasi-isometric to a Coxeter group but is not abstractly commensurabl…
Sylow synchronization in finite groups: the good case
本文证明有限可解群在特定Sylow子群交集条件下存在同步化元素，覆盖奇数阶群并统一旧结果，同时完成对称群、交错群及单群猜想的证明。
Near full groups of bounded type: full group completion
研究有界类型群的子类，由布拉特雷图平铺膨胀产生的有限生成群，在自然局部化假设下添加有限变换可得拓扑全群，在额外假设下原群在拓扑全群中有有限指数甚至重合。
Finitely and non-finitely related words
本文利用链字、冠字词和漩涡字构造非有限相关幂零幺半群，揭示有限相关与非有限相关半群及簇之间的多种反例现象。
The Grunwald problem and homogeneous spaces with non-solvable stabilisers
该研究解决了一类新非可解有限群的Grunwald问题，证明其满足Brauer-Manin障碍为弱逼近唯一障碍的(BM)条件，还探究了小阶群的(BM)性质。
Every finite simple group can be generated by two elements, and in 2000, Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group every nontrivial element belongs to a generating pair. Groups with this property are said to be $\frac{3}{2}$-generated. Which finite groups are $\frac{3}{2}$-generated? Every proper quotient of a $\frac{3}{2}$-generated group is cyclic, and in 2008, Breuer, Guralnick and Kantor made the striking conjecture that this condition alone provides a complete characterisation of the finite groups with this property. This conjectur…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。