59 research outputs found
On Property (FA) for wreath products
We characterize permutational wreath products with Property (FA). For
instance, the standard wreath product A wr B of two nontrivial countable groups
A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely
generated group with finite abelianisation. We also prove an analogous result
for hereditary Property (FA). On the other hand, we prove that many wreath
products with hereditary Property (FA) are not quotients of finitely presented
groups with the same property.Comment: 12 pages, 0 figur
Strongly bounded groups and infinite powers of finite groups
We define a group as strongly bounded if every isometric action on a metric
space has bounded orbits. This latter property is equivalent to the so-called
uncountable strong cofinality, recently introduced by G. Bergman.
Our main result is that G^I is strongly bounded when G is a finite, perfect
group and I is any set. This strengthens a result of Koppelberg and Tits. We
also prove that omega_1-existentially closed groups are strongly bounded.Comment: 10 pages, no figure. Versions 1-3 were entitled "Uncountable groups
with Property (FH)". To appear in Comm. Algebr
A simultaneous generalization of independence and disjointness in boolean algebras
We give a definition of some classes of boolean algebras generalizing free
boolean algebras; they satisfy a universal property that certain functions
extend to homomorphisms. We give a combinatorial property of generating sets of
these algebras, which we call n-independent. The properties of these classes
(n-free and omega-free boolean algebras) are investigated. These include
connections to hypergraph theory and cardinal invariants on these algebras.
Related cardinal functions, Ind, which is the supremum of the cardinalities
of n-independent subsets; i_n, the minimum size of a maximal n-independent
subset; and i_omega, the minimum size of an omega-independent subset, are
introduced and investigated. The values of i_n and i_omega on P(omega)/fin are
shown to be independent of ZFC.Comment: Sumbitted to Orde
A representation theorem for MV-algebras
An {\em MV-pair} is a pair where is a Boolean algebra and is
a subgroup of the automorphism group of satisfying certain conditions. Let
be the equivalence relation on naturally associated with . We
prove that for every MV-pair , the effect algebra is an MV-
effect algebra. Moreover, for every MV-effect algebra there is an MV-pair
such that is isomorphic to
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