Results 121 to 130 of about 10,909 (156)

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 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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Homology of the Infinite Symmetric Group

The Annals of Mathematics, 1961
H*(S(co); Z.,) with coefficients in the integers mod p (p :prime). It is proved that the height of any non-zero element is co if p = 2, and is either co or < p if p is odd. If p = 2 this fact and the result in [11, ? 6] enable us to determine the structure of the cohomology algebra H*(S(oo); Z2) by using Borel's theorem on the structure of Hopf ...
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The group algebra of the infinite symmetric group

Israel Journal of Mathematics, 1976
The rational group algebra of the infinite symmetric group is studied using Young diagrams. Maximal and prime ideals are characterized and the maximal condition on ideals is proved.
Formanek, Edward, Lawrence, John
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Representations of the Infinite Symmetric Group

2016
Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group,
Alexei Borodin, Grigori Olshanski
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The K -functor (Grothendieck group) of the infinite symmetric group

Journal of Soviet Mathematics, 1985
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 123, 126-151 (Russian) (1983; Zbl 0521.20006).
Vershik, A. M., Kerov, S. V.
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Actions of the Infinite Symmetric Group

2003
[no abstract] ; © 2003 Cambridge University Press.
Henson, C. Ward, Iovino, José, Kechris, Alexander S., Odell, Edward   +3 more
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Stable representations of the infinite symmetric group

Izvestiya: Mathematics, 2015
We study the notion of a stable unitary representation of a group (or a -representation of a -algebra) with respect to some group of automorphisms of the group (or algebra). In the case of the group of finitary permutations of a countable set we give a complete description, up to quasi-equivalence, of the representations which are stable with respect ...
A M Vershik, N I Nessonov
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Lévy–Khinchin formula for the infinite symmetric group

Mathematische Zeitschrift, 2012
A function \(f\) on a group \(G\) is said to be a positive type function if, for any \(g_1, g_2, \dotsc, g_n\in G\) and \(c_1, c_2, \dotsc, c_n\in \mathbb{C}\) \[ \sum_{i, j=1}^n c_i \overline{c_j} f(g_i^{-1}g_j)\geq 0. \] Also, a function \(\psi\) on \(G\) is said to be a negative type function if \(\psi(e)\geq 0\), \(\psi(g^{-1})=\overline{\psi(g)}\)
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Infinite symmetric groups

2019
In this work, infinite similarities of permutation groups are investigated by means of new methods. For this purpose, we handle distinct groups on the set of natural numbers and we give the separation of the subgroups of them. Afterwards, we give the matrix representation of this groups.
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