Results 221 to 230 of about 5,571,269 (248)

The Primitive Permutation Groups of Odd Degree

Journal of the London Mathematical Society, 1985
Using the recent classification of finite simple groups all the primitive permutation groups of odd degree are determined. Of course, the case of a regular normal p-group is left unprecise. Without the classification, the proof determines all the primitive groups of odd degree whose socle is a product of known simple groups.
Liebeck, Martin W., Saxl, Jan
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SUBORBITS IN INFINITE PRIMITIVE PERMUTATION GROUPS

Bulletin of the London Mathematical Society, 2001
For every infinite cardinal κ, we construct a primitive permutation group which has a finite suborbit paired with a suborbit of size κ. This answers a question of Peter M. Neumann.
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On Simply Transitive Primitive Permutation Groups

Canadian Journal of Mathematics, 1969
In (1) we considered finite primitive permutation groups G with regular abelian subgroups H satisfying the following hypothesis:(*) H = A × B × C, where A is cyclic of prime power order pα ≠ 4, B has exponent pβ < pα, and C has order prime to p.We remark that an abelian group fails to satisfy (*) (apart from the minor exception associated with the ...
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The Finite Primitive Permutation Groups of Rank Three

Bulletin of the London Mathematical Society, 1986
Let G be a finite primitive permutation group of degree n and rank three. It is readily seen that one of the following holds: (i) \(T\times T\triangleleft G\leq T_ 0 wr Z_ 2\), where \(T_ 0\) is a 2-transitive group of degree \(n_ 0\), the socle T of \(T_ 0\) is simple and \(n=n^ 2_ 0\); (ii) G is an affine group; (iii) the socle L of G is simple.
Liebeck, Martin W., Saxl, Jan
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ON PRIMITIVE SHARP PERMUTATION GROUPS

Communications in Algebra, 2002
ABSTRACT A permutation group is sharp if , where . We deduce a restriction for the structure of primitive sharp groups, namely, that their socle is either regular or nonabelian simple.
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Primitive Permutation Groups of Finite Morley Rank

Proceedings of the London Mathematical Society, 1995
A version is given of the O'Nan-Scott Theorem for definably primitive permutation groups of finite Morley rank. This raises questions about structures of the form \((F,+, \cdot, H)\) where \((F, +, \cdot)\) is an algebraically closed field and \(H\) is a predicate for a central extension of a simple group, with \(H \leq \text{GL} (n,F)\). Among partial
Macpherson, Dugald, Pillay, Anand
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Doubly Transitive But not Doubly Primitive Permutation Groups

Journal of the London Mathematical Society, 1974
+ l preserve asblock desig inn which X = I and k = q + l. Anothe irs exampl PSL(«,q), ne > 2,which preserves a block design in which X = 1 and k = q + l. In these cases the blocksare the line os f the corresponding unitary and projective spaces It i eass .y to see thatno grou opf automorphism ofs a block desig in whicn h X = 1 can ac doublt ...
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The Inclusion Problem for Finite Primitive Permutation Groups

Proceedings of the London Mathematical Society, 1990
The O'Nan Scott Theorem for finite primitive permutation groups identifies various ``types'' of primitive groups, for example an almost simple primitive group G is one satisfying \(T\leq G\leq Aut T\) for some nonabelian simple group T, and a primitive group of affine type is a group \(G=NH\) where N is the additive group of a finite vector space and H
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ON A CONJECTURE ON THE PERMUTATION CHARACTERS OF FINITE PRIMITIVE GROUPS

Bulletin of the Australian Mathematical Society, 2019
Let$G$be a finite group with two primitive permutation representations on the sets$\unicode[STIX]{x1D6FA}_{1}$and$\unicode[STIX]{x1D6FA}_{2}$and let$\unicode[STIX]{x1D70B}_{1}$and$\unicode[STIX]{x1D70B}_{2}$be the corresponding permutation characters. We consider the case in which the set of fixed-point-free elements of$G$on$\unicode[STIX]{x1D6FA}_{1 ...
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On primitive permutation groups with nontrivial global stabilizers

Proceedings of the Steklov Institute of Mathematics, 2008
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