منابع مشابه
Stable pseudofinite groups
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We discuss the Bohr compactification of a pseudofinite group, motivated by a question of Boris Zilber. Basically referring to results in the literature we point out that (i) the Bohr compactification of an ultraproduct of finite simple groups is trivial, and (ii) the “definable” Bohr compactification of any pseudofinite group G, relative to an ambient nonstandard model of set theory in which it...
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We consider groups G interpretable in a supersimple finite rank theory T such that T eq eliminates ∃∞. It is shown that G has a definable soluble radical. If G has rank 2, then if G is pseudofinite it is soluble-by-finite, and partial results are obtained under weaker hypotheses, such as unimodularity of the theory. A classification is obtained when T is pseudofinite and G has a definable and d...
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We show that any pseudofinite group with NIP theory and with a finite upper bound on the length of chains of centralisers is soluble-by-finite. In particular, any NIP rosy pseudofinite group is soluble-by-finite. This generalises, and shortens the proof of, an earlier result for stable pseudofinite groups. An example is given of an NIP pseudofinite group which is not soluble-by-finite. However,...
متن کاملStrongly minimal pseudofinite structures
In this note we point out that any strongly minimal pseudofinite structure (or set) is unimodular in the sense of [1], [5], [2], and hence measurable in the sense of Macpherson and Steinhorn [3], [2] as well as 1-based. The argument, involving nonstandard finite cardinalities, is straightforward. A few people asked about this issue in private conversations and communications, in particular Mart...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2013
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt-2013-0006