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...ion]] of <math>G</math> as a group of [[permutation]]s, or as a group of [[permutation matrices]]. The term also refers to the combination of the two. ==Abstract permutation representation== ...

...all a [[permutation]] <math>p: \mathbb{N} \to \mathbb{N}</math> an ''Agnew permutation''{{efn|This terminology is used only in this article, to simplify the expla '''Agnew's theorem.''' &nbsp;<math>p</math> is an Agnew permutation <math>\iff</math> for all converging series of real or complex terms <math ...

...227555 }}</ref> He [[conjecture]]d that if <math>G</math> is a [[primitive permutation group]] on a finite set <math>S</math> and <math>G_\alpha</math> denotes th ...Jan Saxl]], and [[Gary Seitz]] using the [[classification of finite simple groups]], in particular the fact that only finitely many [[isomorphism]] types of ...

| title = On the diameter of permutation groups | title = On the diameter of permutation groups ...

...her the centroid and/or the spread of the objects is different between the groups. Hence the test is based on the prior calculation of the distance between a ...result to that gained from random permutations of the objects between the groups. Moreover, whilst PERMANOVA tests for similarity based on a chosen distance ...

...'i''</sub> for each ''i'' between 1 and ''k''. The [[Mathieu group|Mathieu groups]] are important examples. ==Classifications of 2-transitive groups == ...

...When <math>S_n</math> is viewed as the [[group (mathematics)|group]] of [[permutation]]s of the set <math>\{1, 2, \ldots, n\}</math>, and if <math>\lambda = (\la ...b, \ldots\}</math> and <math>\times</math> denotes the [[direct product of groups]]. Abstractly, <math>S_\lambda</math> is isomorphic to the product <math>S ...

...=Fon-Der-Flaass |first2=D. G |date=1995-11-01 |title=Bases for permutation groups and matroids |url=https://dx.doi.org/10.1016/0195-6698%2895%2990035-7 |jour Let <math>P</math> be a [[Permutation group|permutational group]] of <math>\Omega</math>,{{clarify|what’s Omega?| ...

...hard|last=Stanley|year=1984}} in his study of the [[symmetric group]] of [[permutation]]s. ...duced decompositions of permutations, and in particular his proof that the permutation ''w''₀ = ''n''(''n'' &minus; 1)...21 (written here in [[one-line ...

...al of the [[sporadic simple group]]s were discovered as rank 3 permutation groups. The primitive rank 3 permutation groups are all in one of the following classes: ...

...algebra]] and [[finite geometry]], the '''list of transitive finite linear groups''' is an important classification of certain highly symmetric [[Group actio ...vides a complete <!-- and irredundant? --> list of the finite 2-transitive groups whose socle is [[elementary abelian group|elementary abelian]]. ...

...rview of various diagram algebras generalizing group algebras of symmetric groups, see Halverson and Ram 2005.</ref> it is natural to write maps on the right ...as [[Schur–Weyl duality]], which is an important application of the place-permutation action.</ref> on <math>n</math> letters, with compositions computed from ri ...

...natural representation of elements of <math>S(m,n)</math> as [[generalized permutation matrices]], where the nonzero entries are ''m''-th [[roots of unity]]: <mat ...Himmet | last = Can | title = Representations of the Generalized Symmetric Groups | journal = Contributions to Algebra and Geometry | volume = 37 | year = 19 ...

{{short description|Connects the homology of the symmetric groups with mapping spaces of spheres}} ...en the [[sphere spectrum]] and the [[classifying space]]s of the symmetric groups via Quillen's [[plus construction]]. ...

...l=https://cordis.europa.eu/project/rcn/210050/factsheet/en|title=Growth in Groups and Graph Isomorphism Now}}</ref> ...st=Pyber|first=László|title=On the orders of doubly transitive permutation groups, elementary estimates|journal=Journal of Combinatorial Theory, Series A|vol ...

...ath>(G, \le_G)</math> and <math>(H, \le_H)</math>, an '''isomorphism of po-groups''' from <math>(G,\leq_G)</math> to <math>(H,\le_H)</math> is an order isomo | title = Notes on infinite permutation groups ...

...by permuting the positions in each tableau (for instance there is a cyclic permutation the cycles the entries of the first row one place forward). ...n each row separately (this "[[Young subgroup]]" is a product of symmetric groups, one for each row). The Young tabloid of ''T'' is denoted {''T''}. ...

Let {{math|''H''}} and {{math|''A''}} be groups, let {{math|''K''&nbsp;{{=}}&nbsp;''A''^''H''}} be the set of all ...',}} then there is an [[Injective function|injective]] [[homomorphism]] of groups <math>\theta:G\to A\wr H</math> such that {{math|''A''}} maps [[Surjective ...

==Definition for finite groups== ...nski|first3=Grigori|title=Asymptotics of Plancherel measures for symmetric groups|journal=Journal of the American Mathematical Society|year=2000|series=13:49 ...

...=275 = 1 + 112 + 162}} vertices. It fixes a [[Conway group#Other sporadic groups|2-2-3 triangle]] in the [[Leech lattice]] and thus is a subgroup of the [[C ...sub>. An outer automorphism interchanges the two classes of M₂₂ groups. This outer automorphism is realized on McL embedded as a subgroup of Co<su ...