Finite simple groups and finite primitive permutation groups
نویسندگان
چکیده
منابع مشابه
Finite Permutation Groups and Finite Simple Groups
In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both wi...
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Let G be a primitive permutation group on a finite set ft, and, for k ^ 2, let G be the Ar-closure of G, that is, the largest subgroup of Sym (ft) preserving all the G-invariant ^-relations on ft. Suppose that G<H^ G and G and H have different socles. It is shown that k ^ 5 and the groups G and H are classified explicitly.
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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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1 Multiply transitive groups Theorem 1.1. Let Ω be a finite set and G ≤ Sym(Ω) be 2–transitive. Let N E G be a minimal normal subgroup. Then one of the following holds: (a) N is regular and elementary abelian. (b) N is primitive, simple and not abelian. Proof. First we show that N is unique. Suppose that M is another minimal normal subgroup of G, so N ∩M = {e} and therefore [N,M ] = {e}. Since ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1983
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700021080