Decision problems for soluble groups of finite rank
نویسندگان
چکیده
منابع مشابه
Linear representations of soluble groups of finite Morley rank
Sufficient conditions are given for groups of finite Morley rank having non-trivial torsion-free nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsion-free Fitting subgroups have faithful linear representations. On the way, using a notion of definable weight space, we prove that certain...
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Article history: Received 21 January 2013 Available online 16 July 2013 Communicated by Derek Holt
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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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Now assume |G : H| is infinite and that H is definable in G (but H need no longer be infinite or G-normal). Let Z = Z◦(G), and note that (a) implies that Z is infinite. If |Z : H ∩Z| is infinite, then |HZ : H| is infinite as well. In this case we are done since H ≤ HZ ≤ NG(H). Otherwise, |Z : H ∩Z| is finite, so the connectedness of Z implies that Z ≤ H. We can now proceed by induction on the r...
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We prove a version of the O'Nan-Scott Theorem for detinably primitive permutation groups of finite Morley rank. This yields questions about structures of finite Morley rank of the form (F, + , . , / / ) where (F, +,.) is an algebraically closed field and H is a central extension of a simple group with /Y=sGL(rt, F). We obtain partial results on such groups H, and show for example that if char(/...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1986
ISSN: 0019-2082
DOI: 10.1215/ijm/1256044628