On closed subgroups of the group of homeomorphisms of a manifold

Frédéric Le Roux

Displaying similar documents to “On closed subgroups of the group of homeomorphisms of a manifold”

On normal subgroups of compact groups

Nikolay Nikolov, Dan Segal (2014)

Journal of the European Mathematical Society

Similarity:

Among compact Hausdorff groups $G$ whose maximal profinite quotient is finitely generated, we characterize those that possess a proper dense normal subgroup. We also prove that the abstract commutator subgroup $[H, G]$ is closed for every closed normal subgroup $H$ of $G$ .

Finite Groups with some $s$ -Permutably Embedded and Weakly $s$ -Permutable Subgroups

Fenfang Xie, Jinjin Wang, Jiayi Xia, Guo Zhong (2013)

Confluentes Mathematici

Similarity:

Let $G$ be a finite group, $p$ the smallest prime dividing the order of $G$ and $P$ a Sylow $p$ -subgroup of $G$ with the smallest generator number $d$ . There is a set $ℳ_{d} (P) = {P_{1}, P_{2}, \dots, P_{d}}$ of maximal subgroups of $P$ such that $⋂_{i = 1}^{d} P_{i} = Φ (P)$ . In the present paper, we investigate the structure of a finite group under the assumption that every member of $ℳ_{d} (P)$ is either $s$ -permutably embedded or weakly $s$ -permutable in $G$ to give criteria for a group to be $p$ -supersolvable or $p$ -nilpotent.

Compactifications of ℕ and Polishable subgroups of $S_{\infty}$

Todor Tsankov (2006)

Fundamenta Mathematicae

Similarity:

We study homeomorphism groups of metrizable compactifications of ℕ. All of those groups can be represented as almost zero-dimensional Polishable subgroups of the group $S_{\infty}$ . As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of $S_{\infty}$ . We prove a sufficient condition for these groups to be one-dimensional and also study their descriptive complexity. In the last section we associate with every Polishable ideal on ℕ...

Modular representations of finite groups with trivial restriction to Sylow subgroups

Paul Balmer (2013)

Journal of the European Mathematical Society

Similarity:

Let $k$ be a field of characteristic $p$ . Let $G$ be a finite group of order divisible by $p$ and $P$ a $p$ -Sylow subgroup of $G$ . We describe the kernel of the restriction homomorphism $T (G) \to T (P)$ , for $T (-)$ the group of endotrivial representations. Our description involves functions $G \to k^{\times}$ that we call weak $P$ -homomorphisms. These are generalizations to possibly non-normal $P \leq G$ of the classical homomorphisms $G / P \to k^{\times}$ appearing in the normal case.

A note on sumsets of subgroups in $ℤ *_{p}$

Derrick Hart (2013)

Acta Arithmetica

Similarity:

Let A be a multiplicative subgroup of $ℤ *_{p}$ . Define the k-fold sumset of A to be $k A = x_{1} + . . . + x_{k} : x_{i} \in A, 1 \leq i \leq k$ . We show that $6 A \supseteq ℤ *_{p}$ for $| A | > p^{11 / 23 + ϵ}$ . In addition, we extend a result of Shkredov to show that ${| 2 A | ≫ | A |}^{8 / 5 - ϵ}$ for $| A | ≪ p^{5 / 9}$ .

On some metabelian 2-groups and applications I

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous (2016)

Colloquium Mathematicae

Similarity:

Let G be some metabelian 2-group satisfying the condition G/G’ ≃ ℤ/2ℤ × ℤ/2ℤ × ℤ/2ℤ. In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem for the 2-ideal classes of some fields k satisfying the condition $G a l (k ₂^{(2)} / k) ≃ G$ , where $k ₂^{(2)}$ is the second Hilbert 2-class field of k.

On $R$ -conjugate-permutability of Sylow subgroups

Xianhe Zhao, Ruifang Chen (2016)

Czechoslovak Mathematical Journal

Similarity:

A subgroup $H$ of a finite group $G$ is said to be conjugate-permutable if $H H^{g} = H^{g} H$ for all $g \in G$ . More generaly, if we limit the element $g$ to a subgroup $R$ of $G$ , then we say that the subgroup $H$ is $R$ -conjugate-permutable. By means of the $R$ -conjugate-permutable subgroups, we investigate the relationship between the nilpotence of $G$ and the $R$ -conjugate-permutability of the Sylow subgroups of $A$ and $B$ under the condition that $G = A B$ , where $A$ and $B$ are subgroups of $G$ . Some results known in the literature are improved...

Waring's number for large subgroups of ℤₚ

Todd Cochrane, Derrick Hart, Christopher Pinner, Craig Spencer (2014)

Acta Arithmetica

Similarity:

Let p be a prime, ℤₚ be the finite field in p elements, k be a positive integer, and A be the multiplicative subgroup of nonzero kth powers in ℤₚ. The goal of this paper is to determine, for a given positive integer s, a value tₛ such that if |A| ≫ tₛ then every element of ℤₚ is a sum of s kth powers. We obtain $t ₄ = p^{22 / 39 + ϵ}$ , $t ₅ = p^{15 / 29 + ϵ}$ and for s ≥ 6, $t ₛ = p^{(9 s + 45) / (29 s + 33) + ϵ}$ . For s ≥ 24 further improvements are made, such as $t_{32} = p^{5 / 16 + ϵ}$ and $t_{128} = p^{1 / 4}$ .

Spectra of elements in the group ring of SU(2)

Alex Gamburd, Dmitry Jakobson, Peter Sarnak (1999)

Journal of the European Mathematical Society

Similarity:

We present a new method for establishing the ‘‘gap” property for finitely generated subgroups of $SU (2)$ , providing an elementary solution of Ruziewicz problem on $S^{2}$ as well as giving many new examples of finitely generated subgroups of $SU (2)$ with an explicit gap. The distribution of the eigenvalues of the elements of the group ring $𝐑 [SU (2)]$ in the $N$ -th irreducible representation of $SU (2)$ is also studied. Numerical experiments indicate that for a generic (in measure) element of $𝐑 [SU (2)]$ , the “unfolded” consecutive...

The Roquette category of finite $p$ -groups

Serge Bouc (2015)

Journal of the European Mathematical Society

Similarity:

Let $p$ be a prime number. This paper introduces the Roquette category $ℛ_{p}$ of finite $p$ -groups, which is an additive tensor category containing all finite $p$ -groups among its objects. In $ℛ_{p}$ , every finite $p$ -group $P$ admits a canonical direct summand $\partial P$ , called the edge of $P$ . Moreover $P$ splits uniquely as a direct sum of edges of Roquette $p$ -groups, and the tensor structure of $ℛ_{p}$ can be described in terms of such edges. The main motivation for considering this category is that the additive functors...

On solvability of finite groups with some $s s$ -supplemented subgroups

Jiakuan Lu, Yanyan Qiu (2015)

Czechoslovak Mathematical Journal

Similarity:

A subgroup $H$ of a finite group $G$ is said to be $s s$ -supplemented in $G$ if there exists a subgroup $K$ of $G$ such that $G = H K$ and $H \cap K$ is $s$ -permutable in $K$ . In this paper, we first give an example to show that the conjecture in A. A. Heliel’s paper (2014) has negative solutions. Next, we prove that a finite group $G$ is solvable if every subgroup of odd prime order of $G$ is $s s$ -supplemented in $G$ , and that $G$ is solvable if and only if every Sylow subgroup of odd order of $G$ is $s s$ -supplemented in $G$ . These results...

A note on infinite $a S$ -groups

Reza Nikandish, Babak Miraftab (2015)

Czechoslovak Mathematical Journal

Similarity:

Let $G$ be a group. If every nontrivial subgroup of $G$ has a proper supplement, then $G$ is called an $a S$ -group. We study some properties of $a S$ -groups. For instance, it is shown that a nilpotent group $G$ is an $a S$ -group if and only if $G$ is a subdirect product of cyclic groups of prime orders. We prove that if $G$ is an $a S$ -group which satisfies the descending chain condition on subgroups, then $G$ is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group...

On malnormal peripheral subgroups of the fundamental group of a $3$ -manifold

Pierre de la Harpe, Claude Weber (2014)

Confluentes Mathematici

Similarity:

Let $K$ be a non-trivial knot in the $3$ -sphere, $E_{K}$ its exterior, $G_{K} = π_{1} (E_{K})$ its group, and $P_{K} = π_{1} (\partial E_{K}) \subset G_{K}$ its peripheral subgroup. We show that $P_{K}$ is malnormal in $G_{K}$ , namely that $g P_{K} g^{- 1} \cap P_{K} = {e}$ for any $g \in G_{K}$ with $g \notin P_{K}$ , unless $K$ is in one of the following three classes: torus knots, cable knots, and composite knots; these are exactly the classes for which there exist annuli in $E_{K}$ attached to $T_{K}$ which are not boundary parallel (Theorem 1 and Corollary 2). More generally, we characterise malnormal peripheral subgroups in the fundamental...

On automorphisms fixing subnormal subgroups of soluble groups

Silvana Franciosi, Francesco de Giovanni (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

The group $Aut_{sn}G$ of all automorphisms leaving invariant every subnormal subgroup of the group $G$ is studied. In particular it is proved that $Aut_{sn}G$ is metabelian if $G$ is soluble, and that $Aut_{sn}G$ is either finite or abelian if $G$ is polycyclic.

The Killing Tensors on an $n$ -dimensional Manifold with $S L (n,)$ -structure

Sergey E. Stepanov, Irina I. Tsyganok, Marina B. Khripunova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $S L (n,)$ -structure and discuss possible applications of obtained results in Riemannian geometry.

The vertical prolongation of the projectable connections

Anna Bednarska (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

We prove that any first order $ℱ_{2} ℳ_{m_{1}, m_{2}, n_{1}, n_{2}}$ -natural operator transforming projectable general connections on an $(m_{1}, m_{2}, n_{1}, n_{2})$ -dimensional fibred-fibred manifold $p = (p, p) : (p_{Y} : Y \to Y) \to (p_{M} : M \to M)$ into general connections on the vertical prolongation $V Y \to M$ of $p : Y \to M$ is the restriction of the (rather well-known) vertical prolongation operator $𝒱$ lifting general connections $\bar{Γ}$ on a fibred manifold $Y \to M$ into $𝒱 \bar{Γ}$ (the vertical prolongation of $\bar{Γ}$ ) on $V Y \to M$ .