Intransitive Permutation Group with Bounded Movement

2003 ◽  
Vol 26 (2) ◽  
pp. 181-184
Author(s):  
Mehdi Alaeiyan ◽  
Shaban Sedghi
Keyword(s):  
Permutation Group ◽  
Bounded Movement

scholarly journals The Maximal Number of Orbits of a Permutation Group with Bounded Movement

1999 ◽  
Vol 214 (2) ◽  
pp. 625-630 ◽  
Author(s):  
Jung R. Cho ◽  
Pan Soo Kim ◽  
Cheryl E. Praeger
Keyword(s):  
Permutation Group ◽  
Bounded Movement

scholarly journals Intransitive Permutation Groups with Bounded Movement Having Maximum Degree

2019 ◽  
Vol 16 ◽  
pp. 8272-8279
Author(s):  
Behnam Razzagh
Keyword(s):  
Positive Integer ◽  
Fixed Points ◽  
Permutation Group ◽  
Maximum Degree ◽  
Permutation Groups ◽  
Ams Classification ◽  
Bounded Movement

Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If for each subset of  the size  is bounded, for , we define the movement of g as the max  over all subsets of . In this paper we classified all of permutation groups on set of size 3m + 1 with 2 orbits such that has movement m . 2000 AMS classification subjects: 20B25

scholarly journals Improvement on the bounds of permutation groups with bounded movement

2003 ◽  
Vol 67 (2) ◽  
pp. 249-256 ◽  
Author(s):  
Mehdi Alaeiyan
Keyword(s):  
Positive Integer ◽  
Fixed Points ◽  
Permutation Group ◽  
Infinite Family ◽  
Permutation Groups ◽  
Bounded Movement

Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Then we define the movement of G as, m := move(G) := supΓ{|Γg \ Γ| │ g ∈ G}. Let p be a prime, p ≥ 5. If G is not a 2-group and p is the least odd prime dividing |G|, then we show that n := |Ω| ≤ 4m – p + 3.Moreover, if we suppose that the permutation group induced by G on each orbit is not a 2-group then we improve the last bound of n and for an infinite family of groups the bound is attained.

scholarly journals Intransitive Permutation Groups with Bounded Movement Having Maximum Degree

2019 ◽  
Vol 16 ◽  
pp. 8340-8347
Author(s):  
Behnam Razzagh
Keyword(s):  
Positive Integer ◽  
Fixed Points ◽  
Permutation Group ◽  
Maximum Degree ◽  
Permutation Groups ◽  
Ams Classification ◽  
Bounded Movement

Let G be a permutation group on a set withno fixed points in and let m be a positive integer. If for each subset T of the  size |Tg\T| is bounded, for gEG, we define the movement of g as the max|Tg\T| over all subsets T of . In this paper we classified all of permutation groups on set    of size 3m + 1 with 2 orbits such that has movement m . 2000 AMS classification subjects: 20B25

The complements in an affine group

2013 ◽  
Vol 50 (2) ◽  
pp. 258-265
Author(s):  
Pál Hegedűs
Keyword(s):  
Permutation Group ◽  
Structural Similarity ◽  
Affine Group ◽  
Permutation Module ◽  
Regular Module ◽  
Brauer Characters

In this paper we analyse the natural permutation module of an affine permutation group. For this the regular module of an elementary Abelian p-group is described in detail. We consider the inequivalent permutation modules coming from nonconjugate complements. We prove their strong structural similarity well exceeding the fact that they have equal Brauer characters.

scholarly journals ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP

2021 ◽  
pp. 1-40
Author(s):  
NICK GILL ◽  
BIANCA LODÀ ◽  
PABLO SPIGA
Keyword(s):  
Permutation Group ◽  
Model Theory ◽  
Independent Set ◽  
Maximum Size ◽  
Proper Subset ◽  
Permutation Groups ◽  
Finite Permutation Group ◽  
Pointwise Stabilizer ◽  
Relational Complexity

Abstract Let G be a permutation group on a set $\Omega $ of size t. We say that $\Lambda \subseteq \Omega $ is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset of $\Lambda $ . We define the height of G to be the maximum size of an independent set, and we denote this quantity $\textrm{H}(G)$ . In this paper, we study $\textrm{H}(G)$ for the case when G is primitive. Our main result asserts that either $\textrm{H}(G)< 9\log t$ or else G is in a particular well-studied family (the primitive large–base groups). An immediate corollary of this result is a characterization of primitive permutation groups with large relational complexity, the latter quantity being a statistic introduced by Cherlin in his study of the model theory of permutation groups. We also study $\textrm{I}(G)$ , the maximum length of an irredundant base of G, in which case we prove that if G is primitive, then either $\textrm{I}(G)<7\log t$ or else, again, G is in a particular family (which includes the primitive large–base groups as well as some others).

Some generalized characters associated to a transitive permutation group

2020 ◽  
Vol 23 (3) ◽  
pp. 393-397
Author(s):  
Wolfgang Knapp ◽  
Peter Schmid
Keyword(s):  
Positive Integer ◽  
Permutation Group ◽  
Frobenius Group ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Transitive Permutation Group ◽  
Point Stabilizer ◽  
Necessary And Sufficient ◽  
Regular Character ◽  
Permutation Character

AbstractLet G be a finite transitive permutation group of degree n, with point stabilizer {H\neq 1} and permutation character π. For every positive integer t, we consider the generalized character {\psi_{t}=\rho_{G}-t(\pi-1_{G})}, where {\rho_{G}} is the regular character of G and {1_{G}} the 1-character. We give necessary and sufficient conditions on t (and G) which guarantee that {\psi_{t}} is a character of G. A necessary condition is that {t\leq\min\{n-1,\lvert H\rvert\}}, and it turns out that {\psi_{t}} is a character of G for {t=n-1} resp. {t=\lvert H\rvert} precisely when G is 2-transitive resp. a Frobenius group.

On a conjecture of Hughes

1967 ◽  
Vol 63 (3) ◽  
pp. 647-652 ◽  
Author(s):  
Judita Cofman
Keyword(s):  
Projective Plane ◽  
Permutation Group ◽  
Translation Plane ◽  
Collineation Group ◽  
Affine Plane ◽  
Finite Projective Plane ◽  
Transitive Permutation Group ◽  
Condition C

D. R. Hughes stated the following conjecture: If π is a finite projective plane satisfying the condition: (C)π contains a collineation group δ inducing a doubly transitive permutation group δ* on the points of a line g, fixed under δ, then the corresponding affine plane πg is a translation plane.

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