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Topic: Symmetric group

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  PlanetMath: symmetric group
We call this group the symmetric group and it is often denoted
Cross-references: cycle notation, finite, structure, group, composition, bijective functions, permutations
This is version 2 of symmetric group, born on 2003-11-10, modified 2003-11-29.
planetmath.org /encyclopedia/SymmetricGroup2.html   (92 words)

 20: Group Theory and Generalizations
Group theory can be considered the study of symmetry: the collection of symmetries of some object preserving some of its structure forms a group; in some sense all groups arise this way.
Groups acting on topological spaces are the basis of equivariant topology and homotopy theory in Algebraic Topology.
Nielsen's theorem: subgroups of free groups are free.
www.math.niu.edu /~rusin/known-math/index/20-XX.html   (2774 words)

 Normal Subgroup of the Symmetric Groups   (Site not responding. Last check: 2007-11-06)
PlanetMath: alternating group is a normal subgroup of the symmetric group...
IngentaConnect Subgroup Embeddings in the Symmetric Group of Degree Nine...
On the group of weak automorphisms of a family of...
www.scienceoxygen.com /math/268.html   (110 words)

 Symmetric group - SmartyBrain Encyclopedia and Dictionary
is a group homomorphism ({+1,-1} is a group under multiplication).
Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)
Linear and Projective Representations of Symmetric Groups (Cambridge Tracts in Mathematics)
smartybrain.com /index.php/Symmetric_group   (631 words)

 Symmetric group - Wikipedia, the free encyclopedia
Applying f after g maps 1 to 2, and then to itself; 2 to 5 to 4; 3 to 4 to 5, and so on.
is a group homomorphism ({+1,-1} is a group under multiplication, where +1 is e, the neutral element).
See cube for the proper rotations of a cube, which form a group isomorphic with S
en.wikipedia.org /wiki/Symmetric_group   (480 words)

 [No title]   (Site not responding. Last check: 2007-11-06)
Combinatorially, we view this class of symmetric tensegrities as having one vertex for each element of the underlying group G and 3 combinatorially distinct basic edges (or edge pairs, really) coming out of the basepoint vertex.
The catalogue is organized by the type of abstract group of symmetries of the underlying tensegrity.
But one must realize that for each of these groups, there is more than one representation of that group as a group of symmetries of a Euclidean space.
mathlab.cit.cornell.edu /visualization/tenseg/tenseg.html   (1441 words)

 Youngs's Representations of the Symmetric Group (ResearchIndex)   (Site not responding. Last check: 2007-11-06)
Abstract: We describe the di erent matrices, due to Young, representing the symmetric group, by reading the same graph with various labellings.
210 The representation theory of the symmetric group (context) - JAMES - 1981
Group Actions on Arrangements of Linear Subspaces and..
citeseer.ist.psu.edu /lascoux00youngss.html   (310 words)

 Schur Group Theory Software
Schur is a stand alone C program for interactively calculating properties of Lie groups and symmetric functions.
As well as being a research tool Schur forms an excellent tool for helping students to independently explore the properties of Lie groups and symmetric functions and to test their understanding by creating simple examples and moving on to more complex examples.
The standardisation of non-standard representations of groups by the use of modification procedures.
smc.vnet.net /Schur.html   (1154 words)

 GAP Manual: 1.29 About Defining New Parametrized Domains
The most important knowledge for a permutation group is a base and a strong generating set with respect to that base.
One of the things that are very easy for symmetric groups is the computation of centralizers of elements.
This is very easy, because two elements are conjugated in a symmetric group when they have the same cycle structure.
www-groups.dcs.st-and.ac.uk /gap/Gap3/Manual3/C001S029.htm   (615 words)

 Symmetry Group   (Site not responding. Last check: 2007-11-06)
Thus when we are considering the symmetry group of such a figure we may suppose G to be generated by rotations and, perhaps, reflexions.
It is easy to see why the symmetry groups are the same; for the centers of the faces of a cube are the vertices of a regular octahedron, and the centers of the faces of a regular octahedron are the vertices of a cube.
It is a matter of great interest and relevance here that the symmetries of the Diagonal Cube and the special braided octahedron of Figure 7 and Figure 16, respectively (of [Rec]) each permute the four braided strips from which the models are made.
www.mi.sanu.ac.yu /vismath/hil/ped3.htm   (1390 words)

 Citebase - Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables   (Site not responding. Last check: 2007-11-06)
We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan.
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables.
We uncover the structure of the space of symmetric functions in non-commutative variables by showing that the underlined Hopf algebra is both free and co-free.
citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0502082   (1164 words)

 Citebase - Point Processes and the Infinite Symmetric Group. Part II: Higher Correlation Functions   (Site not responding. Last check: 2007-11-06)
We study a 3-parametric family of stochastic point processes on the one-dimensional lattice originated from a remarkable family of representations of the infinite symmetric group.
The infinite-dimensional unitary group U(infinity) is the inductive limit of growing compact unitary groups U(N).
The latter has infinite dimension and is a kind of dual object for the infinite symmetric group.
citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/9804087   (1024 words)

 Research   (Site not responding. Last check: 2007-11-06)
If you don't know what a group is then click here for a definition.
Those groups that have just one (finite) non-abelian composition factor up to isomorphism are listed in the first seven sections according to the isomorphism type of this composition factor.
Soluble groups and groups with at least two non-isomorphic non-abelian composition factors are listed under `other groups'.
web.mat.bham.ac.uk /J.N.Bray/res.html   (227 words)

A new approach to the character theory of the symmetric group has been developed during the past fifteen years which is in many ways more efficient, more transparent, and more elementary.
In this approach, to each permutation is assigned a class function of the corresponding symmetric group.
The three detailed appendices on group characters, the Solomon descent algebra and the Robinson—Schensted correspondence makes the material self-contained and suitable for undergraduate level.
www.worldscibooks.com /mathematics/p369.html   (333 words)

 GAP Manual: 71 The Specht Share Package
As the (modular) representation theory of these algebras closely resembles that of the (modular) representation theory of the symmetric groups --- indeed, the later is a special case of the former --- many of the combinatorial tools from the representation theory of the symmetric group are included in the package.
is the Hecke algebras analogue of the characteristic of the field in the modular representation theory of finite groups.
The Fock space F is an (integrable) module for the quantum group U_q(widehat{sl}_{}) of the affine special linear group.
schmidt.ucg.ie /gap/CHAP071.htm   (7123 words)

 Powell's Books - Symmetric Group 2ND Edition Representations Comb by Bruce Eli Sagan
This is an introduction to the representation theory of the symmetric group from three different points of view: via general representation theory, via combinatorial algorithms, and via symmetric functions.
This text is an introduction to the representation theory of the symmetric group from three different points of view: via general representation theory, via combinatorial algorithms, and via symmetric functions.
The style of presentation is relaxed yet rigorous and the prerequisites have been kept to a minimumundergraduate courses in linear algebra and group theory will suffice.
www.powells.com /biblio?isbn=0387950672   (382 words)

 Symmetric Group Generation and Shuffle Permutations   (Site not responding. Last check: 2007-11-06)
Their study may touch a number of areas: Markov chains, random walks, statistics, asymptotics and algorithmic group theory.
In particular, we outline the complex Schreier-Sims algorithm and its importance in solving polynomially many problems in permutation groups.
A well-known theorem shows that, probabilistically, the symmetric group can be very easily generated using two random permutations.
www.ii.uib.no /~pinar/seminar/fabio.html   (112 words)

 Symmetric, Alternating and Permutation groups
then we customarily write the symmetric group as
is a subgroup of a symmetric group on some set
Recall that the cycle (1 2 3) can also be written as (3 1 2) or (2 3 1).
www.math.csusb.edu /notes/advanced/algebra/gp/node10.html   (394 words)

 Amazon.ca: Books: The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions   (Site not responding. Last check: 2007-11-06)
Introduces the theory of the symmetric group, using three different points of view: general representation theory, combinatorial algorithms, and symmetric functions.
I completed all of the exercises, so it is well-paced for this kind of study.
I started with only an introductory knowledge of group theory, so it is self-contained.
www.amazon.ca /exec/obidos/ASIN/0387950672   (406 words)

 Atlas: The amazing infinite symmetric group by George Bergman   (Site not responding. Last check: 2007-11-06)
Suppose G is a group and X a subset of G. For i = 1, 2,..., let X
Details can be found in the two preprints on infinite symmetric groups at http://math.berkeley.edu/~gbergman/papers/, and papers cited in these.
The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caoc-21.
atlas-conferences.com /cgi-bin/abstract/caoc-21   (203 words)

 The symmetric group   (Site not responding. Last check: 2007-11-06)
, in which case we shall denote the symmetric group by
This group is also called the symmetric group on
We can compute all possible products of two elements of the group and tabulate them:
web.usna.navy.mil /~wdj/book/node165.html   (117 words)

 Find in a Library: Representation theory of the symmetric group.
Find in a Library: Representation theory of the symmetric group.
To find a library, type in a postal code, state, province, or country.
WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
www.worldcatlibraries.org /wcpa/ow/0befad3bb673c7a6.html   (39 words)

 Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
Energy Citations Database (ECD) Document #4497176 - Symmetric group and meson Born amplitudes
Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
For a journal article, please see the Resource Relation field.
www.osti.gov /energycitations/product.biblio.jsp?osti_id=4497176   (100 words)

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