Large free subgroups of automorphism groups of ultrahomogeneous spaces

Szymon Głąb; Filip Strobin

The search session has expired. Please query the service again.

Displaying similar documents to “Large free subgroups of automorphism groups of ultrahomogeneous spaces”

On fixed point free involutions of $R^{1} \times S^{2}$

Gerhard X. Ritter (1976)

Colloquium Mathematicae

Similarity:

On quotients of the space of orderings of the field ℚ(x)

Paweł Gładki, Bill Jacob (2016)

Banach Center Publications

Similarity:

In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings $(X_{ℚ (x)}, G_{ℚ (x)})$ - it is, in general, nontrivial to determine whether, for a subgroup $G ₀ \subset G_{ℚ (x)}$ the derived quotient structure $(X_{ℚ (x)} |_{G ₀}, G ₀)$ is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.

Prescribing endomorphism algebras of $ℵ_{n}$ -free modules

Rüdiger Göbel, Daniel Herden, Saharon Shelah (2014)

Journal of the European Mathematical Society

Similarity:

It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case...

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...

Product decompositions of quasirandom groups and a Jordan type theorem

Nikolay Nikolov, László Pyber (2011)

Journal of the European Mathematical Society

Similarity:

We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If $k$ is the minimal degree of a representation of the finite group $G$ , then for every subset $B$ of $G$ with $| B | > | G | / k^{1 / 3}$ we have $B^{3} = G$ . We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan’s theorem which implies that if $k \geq 2$ , then $G$ has a...

Equalizers and coactions of groups

Martin Arkowitz, Mauricio Gutierrez (2002)

Fundamenta Mathematicae

Similarity:

If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group $_{f} \subseteq G * H$ be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism $p_{f} {= p |}_{f} :_{f} \to G$ . A right inverse (section) $G \to_{f}$ of $p_{f}$ is called a coaction on G. In this paper we study $_{f}$ and the sections of $p_{f}$ . We consider the following topics: the structure of $_{f}$ as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and...

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...

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.

Polycyclic groups with automorphisms of order four

Tao Xu, Fang Zhou, Heguo Liu (2016)

Czechoslovak Mathematical Journal

Similarity:

In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if $α$ is an automorphism of order four of a polycyclic group $G$ and the map $ϕ : G \to G$ defined by $g^{ϕ} = [g, α]$ is surjective, then $G$ contains a characteristic subgroup $H$ of finite index such that the second derived subgroup $H^{''}$ is included in the centre of $H$ and $C_{H} (α^{2})$ is abelian, both $C_{G} (α^{2})$ and $G / [G, α^{2}]$ are abelian-by-finite. These results extend recent and classical results in...

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 $| A | ≪ p^{5 / 9}$ .

The superfocal subgroup

Marian Deaconescu (1984)

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

Similarity:

Nel presente lavoro vengono dimostrati teoremi d'esistenza di $p$ -complementi normali nei gruppi finiti.

On the conjugate type vector and the structure of a normal subgroup

Ruifang Chen, Lujun Guo (2022)

Czechoslovak Mathematical Journal

Similarity:

Let $N$ be a normal subgroup of a group $G$ . The structure of $N$ is given when the $G$ -conjugacy class sizes of $N$ is a set of a special kind. In fact, we give the structure of a normal subgroup $N$ under the assumption that the set of $G$ -conjugacy class sizes of $N$ is $(p_{1 n_{1}}^{a_{1 n_{1}}}, \dots, p_{11}^{a_{11}}, 1) \times \dots \times (p_{r n_{r}}^{a_{r n_{r}}}, \dots, p_{r 1}^{a_{r 1}}, 1)$ , where $r > 1$ , $n_{i} > 1$ and $p_{i j}$ are distinct primes for $i \in {1, 2, \dots, r}$ , $j \in {1, 2, \dots, n_{i}}$ .

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.

On a generalization of a theorem of Burnside

Jiangtao Shi (2015)

Czechoslovak Mathematical Journal

Similarity:

A theorem of Burnside asserts that a finite group $G$ is $p$ -nilpotent if for some prime $p$ a Sylow $p$ -subgroup of $G$ lies in the center of its normalizer. In this paper, let $G$ be a finite group and $p$ the smallest prime divisor of $| G |$ , the order of $G$ . Let $P \in {Syl}_{p} (G)$ . As a generalization of Burnside’s theorem, it is shown that if every non-cyclic $p$ -subgroup of $G$ is self-normalizing or normal in $G$ then $G$ is solvable. In particular, if $P ≇ 〈 a, b | a^{p^{n - 1}} = 1, b^{2} = 1, b^{- 1} a b = a^{1 + p^{n - 2}} 〉$ , where $n \geq 3$ for $p > 2$ and $n \geq 4$ for $p = 2$ , then $G$ is $p$ -nilpotent or $p$ -closed. ...

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...