Results 211 to 220 of about 10,433 (250)

Implausible Subgroups of Infinite Symmetric Groups

Bulletin of the London Mathematical Society, 1988
Let S denote the infinite symmetric group of all permutations of \(\omega\), the set of natural numbers. The authors study the possibilities for the induced action of subgroups \(G\subseteq S\) on the power set \({\mathcal P}(\omega)\). Assuming Martin's axiom (MA), they show, in particular, that for any infinite cardinal \(\kappa
Shelah, Saharon, Thomas, Simon
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Maximal Subgroups of Infinite Symmetric Groups

Proceedings of the London Mathematical Society, 1994
This work is concerned with maximal subgroups of \(S=\text{Sym}(\Omega)\) where \(\Omega\) is a set of infinite cardinality \(\kappa\). Known examples include stabilizers of finite sets, ``almost'' stabilizers of infinite sets \(\Sigma\) where \(| \Sigma|< \kappa\), and ``almost'' stabilizers of finite partitions.
Brazil, Marcus, Covington, Jacinta, Penttila, Tim, Praeger, Cheryl E., Woods, Alan R.   +4 more
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SOME MAXIMAL SUBGROUPS OF INFINITE SYMMETRIC GROUPS

The Quarterly Journal of Mathematics, 1996
Several classes of maximal subgroups of symmetric groups \(S=\text{Sym}(\Omega)\) where \(|\Omega|=\kappa\) is infinite are investigated. A collection \(\mathcal I\) of subsets of \(\Omega\) is called an ideal on \(\Omega\) if \(\emptyset\in{\mathcal I}\), \(\Omega\notin{\mathcal I}\), and \(\mathcal I\) is closed under taking subsets and finite unions.
Covington, Jacinta, Macpherson, Dugald, Mekler, Alan   +2 more
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Maximal Subgroups of Infinite Symmetric Groups

Journal of the London Mathematical Society, 1990
It is shown that if G is a permutation group on a countable set X and if G is not highly transitive, then G is contained in some maximal proper subgroup of the full symmetric group on X.
Macpherson, H. D., Praeger, Cheryl E.
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Maximal supersoluble subgroups of symmetric groups

Annali di Matematica Pura ed Applicata, 1991
All maximal supersoluble subgroups of symmetric groups are classified. But, in fact, the main result in this paper is the classification of the maximal supersoluble transitive subgroups of the symmetric group \(S_ n\) on \(n\) letters. The proof of the main result splits into two parts. In Section 4 the authors present a certain general construction of
M. Bianchi, A. Mauri, P. Hauck
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Maximal Subgroups of Infinite Symmetric Groups

Canadian Mathematical Bulletin, 1967
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 ...
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Symmetric subgroups of finite groups

Algebra and Logic, 1984
The author studies finite groups \(G\) generated by a class \(D\) of conjugate involutions which contain a subgroup \(S\) isomorphic to the symmetric group \(S_ n\) such that \(S\cap D=:\Delta\) corresponds to the class of transpositions of \(S_ n\) and \(S\) acts transitively on \(D-\Delta\).
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SYMMETRIC GROUPS AS PRODUCTS OF ABELIAN SUBGROUPS

Bulletin of the London Mathematical Society, 2002
Summary: A proof is given that the full symmetric group over any infinite set is the product of finitely many Abelian subgroups. In fact, 289 subgroups suffice. Sharp bounds are also obtained on the minimal number \(k\), such that the finite symmetric group \(S_n\) is the product of \(k\) Abelian subgroups.
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Equivariant Euler Characteristics of Subgroup Complexes of Symmetric Groups

Annals of Combinatorics, 2022
For a finite group \(G\), the partially ordered set \(S_G^\ast\) of its proper nontrivial subgroups has an action of \(G\) by conjugation. This paper studies the equivariant homotopy type of this \(G\)-poset and its equivariant Euler characteristics for symmetric and alternating groups.
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Maximal Abelian Subgroups of the Symmetric Groups

Canadian Journal of Mathematics, 1971
Our aim is to present some global results about the set of maximal abelian subgroups of the symmetric group Sn. We shall show that certain properties are true for “almost all” subgroups of this set in the sense that the proportion of subgroups which have these properties tends to 1 as n → ∞.
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