منابع مشابه
Semifree actions of free groups
We study countable universes similar to a free action of a group G. It turns out that this is equivalent to the study of free semi-actions of G, with two universes being transformable iff one corresponding free semi-action can be obtained from the other by a finite alteration. In the case of a free group G (in finitely many or countably many generators), a classification is given. Mathematics S...
متن کاملIncomparable Actions of Free Groups
Suppose that X is a standard Borel space, E is a countable Borel equivalence relation on X, and μ is an E-invariant Borel probability measure on X. We consider the circumstances under which for every countable non-abelian free group Γ, there is a Borel sequence (·r)r∈R of free actions of Γ on X, generating subequivalence relations Er of E with respect to which μ is ergodic, with the further pro...
متن کاملConvergence of spherical averages for actions of free groups
Let (X, ν) be a probability space and suppose a free group Fm withm generators acts on (X, ν) by measure-preserving transformations. Let {a1, . . . , am} be a set of free generators for Fm and let T1, . . . , Tm : X → X be transformations corresponding to the generators. Write T−i = T −1 i for i = 1, . . . ,m, and set A = {−m, . . . ,−1, 1, . . . ,m}. We also have the action Fm on L1(X, ν), def...
متن کاملFree Actions of P-groups on Products of Lens Spaces
Let p be an odd prime number. We prove that if (Z/p) acts freely on a product of k equidimensional lens spaces, then r ≤ k. This settles a special case of a conjecture due to C. Allday [6]. We also find further restrictions on non-abelian p-groups acting freely on a product of lens spaces. For actions inducing a trivial action on homology, we reach the following characterization: A p-group can ...
متن کاملFREE ACTIONS OF EXTRASPECIAL p-GROUPS ON S × S
Let p be an odd regular prime, and let Gp denote the extraspecial p–group of order p and exponent p. We show that Gp acts freely and smoothly on S2p−1×S2p−1. For p = 3 we explicitly construct a free smooth action of a Lie group G̃3 containing G3 on S × S. In addition, we show that any finite odd order subgroup of the exceptional Lie group G2 admits a free smooth action on S × S.
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2001
ISSN: 0373-0956
DOI: 10.5802/aif.1819