On primitive solvable permutation groups with commutative stabilizer of a point

1993 ◽  
Vol 34 (5) ◽  
pp. 984-987
Author(s):  
K. K. Shchukin
Keyword(s):  
Permutation Groups ◽  
Stabilizer Of A Point

scholarly journals On primitive permutation groups whose stabilizer of a point induces $L_{2}(q)$ on a suborbit

1976 ◽  
Vol 20 (1) ◽  
pp. 48-64 ◽  
Author(s):  
Ulrich Dempwolff
Keyword(s):  
Permutation Groups ◽  
Stabilizer Of A Point

scholarly journals On doubly transitive permutation groups of degree prime squared plus one

1977 ◽  
Vol 23 (2) ◽  
pp. 202-206 ◽  
Author(s):  
David Chillag
Keyword(s):  
Permutation Group ◽  
Permutation Groups ◽  
Transitive Permutation Group ◽  
Normal Extension ◽  
Stabilizer Of A Point

AbstractA doubly transitive permutation group of degreep2+ 1, pa prime, is proved to be doubly primitive forp≠ 2. We also show that if such a group is not triply transitive then either it is a normal extension ofP S L(2,p2) or the stabilizer of a point is a rank 3 group.

scholarly journals On Permutation Groups of Prime Degree p Which Contain at Least Two Classes of Conjugate Subgroups of Index p. II

1970 ◽  
Vol 37 ◽  
pp. 201-208 ◽  
Author(s):  
Noboru Ito
Keyword(s):  
Permutation Group ◽  
Permutation Groups ◽  
Transitive Permutation Group ◽  
Prime Degree ◽  
Stabilizer Of A Point

Let p be a prime and let Ω be the set of p symbols 1,2, ..., p, called points. Let be a transitive permutation group on Ω such that(I) contains a subgroup of index p which is not the stabilizer of a point.

Compact cellular algebras and permutation groups

1999 ◽  
Vol 197-198 (1-3) ◽  
pp. 247-267 ◽  
Author(s):  
S Evdokimov
Keyword(s):  
Permutation Groups ◽  
Cellular Algebras

A ROUTING ALGORITHM FOR THE CAYLEY GRAPHS GENERATED BY PERMUTATION GROUPS

2020 ◽  
Vol 21 (2) ◽  
pp. 187-194
Author(s):  
А. A. Kuznetsov ◽  
◽  
V. V. Kishkan ◽  
Keyword(s):  
Cayley Graphs ◽  
Routing Algorithm ◽  
Permutation Groups

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).

scholarly journals Permutation groups with small orbit growth

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Manuel Bodirsky ◽  
Bertalan Bodor
Keyword(s):  
Automorphism Group ◽  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Permutation Groups ◽  
First Order ◽  
Finite Covers

Abstract Let K exp + \mathcal{K}_{{\operatorname{exp}}{+}} be the class of all structures 𝔄 such that the automorphism group of 𝔄 has at most c ⁢ n d ⁢ n cn^{dn} orbits in its componentwise action on the set of 𝑛-tuples with pairwise distinct entries, for some constants c , d c,d with d < 1 d<1 . We show that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of finite covers of first-order reducts of unary structures, and also that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of first-order reducts of finite covers of unary structures. It follows that the class of first-order reducts of finite covers of unary structures is closed under taking model companions and model-complete cores, which is an important property when studying the constraint satisfaction problem for structures from K exp + \mathcal{K}_{{\operatorname{exp}}{+}} . We also show that Thomas’ conjecture holds for K exp + \mathcal{K}_{{\operatorname{exp}}{+}} : all structures in K exp + \mathcal{K}_{{\operatorname{exp}}{+}} have finitely many first-order reducts up to first-order interdefinability.

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