Results 191 to 200 of about 1,562 (223)

Permutation polynomials and primitive permutation groups

Archiv Der Mathematik, 1991
In 1966 L. Carlitz conjectured that for every even positive integer \(n\) there exists a constant \(c_ n\) such that for any odd \(q>c_ n\) there is no permutation polynomial of degree \(n\) over the finite field \(F_ q\) of order \(q\). This conjecture was known to hold for \(n\) a power of 2 and for all even \(n\leq 16\). In this paper the conjecture
Stephen D Cohen, Cohen Stephen D
exaly   +2 more sources

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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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
openaire   +1 more source

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