Results 221 to 230 of about 9,212,172 (248)

On the orders of Primitive Permutation Groups

Bulletin of the London Mathematical Society, 1980
CHERYL E. PRAEGE R AN JAD N SAXLThe proble omf bounding the order of a permutation grou G ipn terms of itsdegree n was one of the central problem of 19tsh century group theory (see [4]) It.is closely relate to thde 1860 Grand Prix proble of them Pari s Academy but it, shistory goe isn fact much further back (see e.g an. [3]d [10]), [1] .
Praeger, Cheryl E., Saxl, Jan
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Primitive k-free permutation groups

Archiv Der Mathematik, 2007
For a finite permutation group G acting on a set Ω, we say that G is k-free if the set-wise stabilizer of every k-subset of Ω is trivial.
D Bundy
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Closures of Finite Primitive Permutation Groups

Bulletin of the London Mathematical Society, 1992
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Praeger, Cheryl E., Saxl, Jan
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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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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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