Results 221 to 230 of about 11,025 (250)

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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Subgroup Embeddings in the Symmetric Group of Degree Nine

Journal of Mathematical Sciences, 2002
This note is a continuation of the authors' papers [\textit{P. V. Gavron} and \textit{V. I. Mysovskikh}, Subgroups of the symmetric groups of degree not exeeding seven. In ``Rings and Matrix Groups'', Ordzhonikidze 1984, 35-42 (1984); \textit{V. I. Mysovskikh} and \textit{A. I. Skopin}, Zap. Nauchn. Semin.
Mysovskikh, V. I., Skopin, A. I.
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On regular pronormal subgroups of symmetric groups

Acta Mathematica Hungarica, 1979
exaly   +3 more sources

Normal subgroups of nonstandard symmetric and alternating groups

Archive for Mathematical Logic, 2007
Let \({\mathcal M}\) be a nonstandard model of Peano arithmetic, with domain \(M\), and \(n\in M\) be a nonstandard natural number. Denote by \(S_n\) and \(A_n\) the symmetric and the alternating group of permutations of the internal set \(\{0,1,\dots,n-1\}\), respectively. By the transfer principle, \(S_n\) and \(A_n\) have all the usual properties of
John Allsup, Richard Kaye
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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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ON CERTAIN MAXIMAL SUBGROUPS OF SYMMETRIC AND ALTERNATING GROUPS

Mathematics of the USSR-Sbornik, 1972
This paper deals with the problem of describing the maximal subgroups of symmetric and alternating groups. Certain primitive groups which are not multiply transitive are considered, and it is shown that among these there are infinite series of groups which are maximal in symmetric and alternating groups. Figures: 3. Bibliography: 15 items.
Kaluzhnin, L. A., Klin, M. Kh.
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Derangements in Sylow subgroups of symmetric groups

Ars Comb., 1997
Let \(p\) be a prime, and \(H_n\) a Sylow \(p\)-subgroup in \(S_n\). The authors find a recursive formula that expresses the number \(h_n\) of derangements (i.e.~permutations with no point fixed) in \(H_n\). If \(f_n=h_n/|H_n|\) and \(g_n=(f_1+\cdots+f_n)/n\), then, as they show, the sequence \(g_n\) converges to \(0\), while the set \(\{f_n;\;n\geq 1\}
Brian Peterson, Linda Valdes
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Embedding of Nonprimary Subgroups in the Symmetric Group S 9

Journal of Mathematical Sciences, 2004
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Mysovskikh, V. I., Skopin, A. I.
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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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Combinatorial congruences fromp-subgroups of the symmetric group

Graphs and Combinatorics, 1993
There has been considerable interest in the methods of deriving congruences from group actions; see \textit{G.-C. Rota} and \textit{B. Sagan} [Eur. J. Comb. 1, 67-76 (1980; Zbl 0453.05008)], or \textit{B. Sagan} [J. Number Theory 20, 210-237 (1985; Zbl 0577.10003)]. The author introduces a different approach to this question. Let \(p\) be a prime and \(
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