Finite rank and pseudofinite groups
نویسندگان
چکیده
منابع مشابه
Stable pseudofinite groups
The main theorem is that if G is a pseudofinite group with stable theory, then G has a definable normal soluble subgroup of finite index.
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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,...
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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 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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Introduction. Zilber’s original trichotomy conjecture proposed an explicit classification of all one-dimensional objects arising in model theory. At one point, classifying the simple groups of finite Morley rank was viewed as a subproblem whose affirmative answer would justify this conjecture. Zilber’s conjecture was eventually refuted by Hrushovski [9], and the classification of simple groups ...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2018
ISSN: 1435-4446,1433-5883
DOI: 10.1515/jgth-2018-0007