Factors of ergodic group extensions of rotations

Jan Kwiatkowski

Displaying similar documents to “Factors of ergodic group extensions of rotations”

Isometric extensions, 2-cocycles and ergodicity of skew products

Alexandre Danilenko, Mariusz Lemańczyk (1999)

Studia Mathematica

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We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension $T_{α}$ and admits a prescribed subgroup in the centralizer of $T_{α}$ .

Minimality and unique ergodicity for subgroup actions

Shahar Mozes, Barak Weiss (1998)

Annales de l'institut Fourier

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Let $G$ be an $ℝ$ -algebraic semisimple group, $H$ an algebraic $ℝ$ -subgroup, and $Γ$ a lattice in $G$ . Partially answering a question posed by Hillel Furstenberg in 1972, we prove that if the action of $H$ on $G / Γ$ is minimal, then it is uniquely ergodic. Our proof uses in an essential way Marina Ratner’s classification of probability measures on $G / Γ$ invariant under unipotent elements, and the study of “tubes” in $G / Γ$ .

p-Isomorphisms of an abelian group of order $p^{m}$ .

G. Miller (1915)

Prace Matematyczno-Fizyczne

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The superfocal subgroup

Marian Deaconescu (1984)

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

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

Abelian quasinormal subgroups of groups

Stewart E. Stonehewer, Giovanni Zacher (2004)

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

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Let $G$ be any group and let $A$ be an abelian quasinormal subgroup of $G$ . If $n$ is any positive integer, either odd or divisible by $4$ , then we prove that the subgroup $A^{n}$ is also quasinormal in $G$ .

On $S$ -quasinormal and $c$ -normal subgroups of a finite group

Shirong Li, Yangming Li (2008)

Czechoslovak Mathematical Journal

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Let $ℱ$ be a saturated formation containing the class of supersolvable groups and let $G$ be a finite group. The following theorems are presented: (1) $G \in ℱ$ if and only if there is a normal subgroup $H$ such that $G / H \in ℱ$ and every maximal subgroup of all Sylow subgroups of $H$ is either $c$ -normal or $S$ -quasinormally embedded in $G$ . (2) $G \in ℱ$ if and only if there is a normal subgroup $H$ such that $G / H \in ℱ$ and every maximal subgroup of all Sylow subgroups of $F^{*} (H)$ , the generalized Fitting subgroup of $H$ , is either $c$ -normal...

Tidy subgroups for commuting automorphisms of totally disconnected groups: An analogue of simultaneous triangularisation of matrices.

Willis, George A. (2004)

The New York Journal of Mathematics [electronic only]

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On lattice properties of S-permutably embedded subgroups of finite soluble groups

L. M. Ezquerro, M. Gómez-Fernández, X. Soler-Escrivà (2005)

Bollettino dell'Unione Matematica Italiana

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In this paper we prove the following results. Let π be a set of prime numbers and G a finite π-soluble group. Consider U, V ≤ G and $H \in {Hall}_{π} (G)$ such that $H \cap V \in {Hall}_{π} (V)$ and $1 \neq H \cap U \in {Hall}_{π} (U)$ . Suppose also $H \cap U$ is a Hall π-sub-group of some S-permutable subgroup of G. Then $H \cap U \cap V \in {Hall}_{π} (U \cap V)$ and $〈 H \cap U, H \cap V 〉 \in {Hall}_{π} (〈 U \cap V 〉)$ . Therefore,the set of all S-permutably embedded subgroups of a soluble group G into which a given Hall system Σ reduces is a sublattice of the lattice of all Σ-permutable subgroups of G. Moreover any two subgroups of this sublattice of coprimeorders...