On the List of Finite Primitive Permutation Groups of Degree ≤ 50
نویسندگان
چکیده
منابع مشابه
ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...
متن کاملClosures of Finite Primitive Permutation Groups
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.
متن کاملPrimitive Permutation Groups of Finite Morley Rank
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(/...
متن کاملThe affine primitive permutation groups of degree less than 1000
In this paper we complete the classification of the primitive permutation groups of degree less than 1000 by determining the irreducible subgroups of GL(n, p) for p prime and pn < 1000. We also enumerate the maximal subgroups of GL(8, 2), GL(4, 5) and GL(6, 3). © 2003 Elsevier Science Ltd. All rights reserved. MSC: 20B10; 20B15; 20H30
متن کاملThe primitive permutation groups of degree less than 2500
In this paper we use the O’Nan–Scott Theorem and Aschbacher’s theorem to classify the primitive permutation groups of degree less than 2500. MSC: 20B15, 20B10 1 Historical Background The classification of the primitive permutation groups of low degree is one of the oldest problems in group theory. The earliest significant progress was made by Jordan, who in 1871 counted the primitive permutatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1996
ISSN: 0747-7171
DOI: 10.1006/jsco.1996.0049