scholarly journals A classification of the maximal subgroups of the finite alternating and symmetric groups

1987 ◽  
Vol 111 (2) ◽  
pp. 365-383 ◽  
Author(s):  
Martin W Liebeck ◽  
Cheryl E Praeger ◽  
Jan Saxl
Keyword(s):  
Symmetric Groups ◽  
Maximal Subgroups ◽  
Alternating And Symmetric Groups

scholarly journals A classification of certain maximal subgroups of symmetric groups

2006 ◽  
Vol 304 (2) ◽  
pp. 1108-1113 ◽  
Author(s):  
Benjamin Newton ◽  
Bret Benesh
Keyword(s):  
Symmetric Groups ◽  
Maximal Subgroups

scholarly journals Boolean lattices in finite alternating and symmetric groups

2020 ◽  
Vol 8 ◽  
Author(s):  
Andrea Lucchini ◽  
Mariapia Moscatiello ◽  
Sebastien Palcoux ◽  
Pablo Spiga
Keyword(s):  
Symmetric Group ◽  
Symmetric Groups ◽  
The Other ◽  
Different Types ◽  
Boolean Lattices ◽  
Product Structures ◽  
Alternating And Symmetric Groups ◽  
Regular Partitions ◽  
Lattice Of Subgroups

Abstract Given a group G and a subgroup H, we let $\mathcal {O}_G(H)$ denote the lattice of subgroups of G containing H. This article provides a classification of the subgroups H of G such that $\mathcal {O}_{G}(H)$ is Boolean of rank at least $3$ when G is a finite alternating or symmetric group. Besides some sporadic examples and some twisted versions, there are two different types of such lattices. One type arises by taking stabilisers of chains of regular partitions, and the other arises by taking stabilisers of chains of regular product structures. As an application, we prove in this case a conjecture on Boolean overgroup lattices related to the dual Ore’s theorem and to a problem of Kenneth Brown.

SOME MAXIMAL SUBGROUPS OF INFINITE SYMMETRIC GROUPS

1996 ◽  
Vol 47 (3) ◽  
pp. 297-311 ◽  
Author(s):  
JACINTA COVINGTON ◽  
DUGALD MACPHERSON ◽  
ALAN MEKLER
Keyword(s):  
Symmetric Groups ◽  
Maximal Subgroups

Maximal Subgroups of Infinite Symmetric Groups

1967 ◽  
Vol 10 (3) ◽  
pp. 375-381 ◽  
Author(s):  
Fred Richman
Keyword(s):  
Boolean Algebra ◽  
Symmetric Groups ◽  
Discrete Space ◽  
Maximal Subgroups ◽  
Infinite Set

The purpose of this paper is to extend results of Ball [1] concerning maximal subgroups of the group S(X) of all permutations of the infinite set X. The basic idea is to consider S(X) as a group of operators on objects more complicated than X. The objects we consider here are subspaces of the Stone-Čech compactification of the discrete space X and the Boolean algebra of “big setoids” of X.

Automorphism groups of simply reducible groups

2020 ◽  
pp. 2150088
Author(s):  
Yongzhi Luan
Keyword(s):  
Computer Algebra System ◽  
Coxeter Groups ◽  
Eigenvalue Problems ◽  
Automorphism Groups ◽  
Symmetric Groups ◽  
Molecular Symmetry ◽  
Dihedral Groups ◽  
Inner Automorphism ◽  
The Moment

Simply reducible groups are closely related to the eigenvalue problems in quantum theory and molecular symmetry in chemistry. Classification of simply reducible groups is still an open problem which is interesting to physicists. Since there are not many examples of simply reducible groups in literature at the moment, we try to find some examples of simply reducible groups as candidates for the classification. By studying the automorphism and inner automorphism groups of symmetric groups, dihedral groups, Clifford groups and Coxeter groups, we find some new examples of candidates. We use the computer algebra system GAP to get most of these automorphism and inner automorphism groups.

Rational permutation groups containing a full cycle

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Temha Erkoç ◽  
Utku Yilmaztürk
Keyword(s):  
Symmetric Group ◽  
Proper Subgroup ◽  
Symmetric Groups ◽  
Transitive Permutation Group ◽  
Rational Group ◽  
Prime Degree ◽  
A Finite Group ◽  
Rational Groups ◽  
Complex Characters

AbstractA finite group whose irreducible complex characters are rational valued is called a rational group. Thus, G is a rational group if and only if N G(〈x〉)/C G(〈x〉) ≌ Aut(〈x〉) for every x ∈ G. For example, all symmetric groups and their Sylow 2-subgroups are rational groups. Structure of rational groups have been studied extensively, but the general classification of rational groups has not been able to be done up to now. In this paper, we show that a full symmetric group of prime degree does not have any rational transitive proper subgroup and that a rational doubly transitive permutation group containing a full cycle is the full symmetric group. We also obtain several results related to the study of rational groups.

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