Topic

# Symmetric group

About: Symmetric group is a(n) research topic. Over the lifetime, 7945 publication(s) have been published within this topic receiving 134099 citation(s).

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01 Jan 1959

Abstract: Introduction Normal subgroups and homomorphisms Elementary theory of abelian groups Sylow theorems Permutation groups Automorphisms Free groups Lattices and composition series A theorem of Frobenius solvable groups Supersolvable and nilpotent groups Basic commutators The theory of $p$-groups regular $p$-groups Further theory of abelian groups Monomial representations and the transfer Group extensions and cohomology of groups Group representation Free and amalgamated products The Burnside problem Lattices of subgroups Group theory and projective planes Bibliography Index Index of special symbols.

2,957 citations

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01 Jan 1984

Abstract: 1. Symmetric groups and their young subgroups 2. Ordinary irreducible representations and characters of symmetric and alternating groups 3. Ordinary irreducible matrix representations of symmetric groups 4. Representations of wreath products 5. Applications to combinatories and representation theory 6. Modular representations 7. Representation theory of Sn over an arbitrary field 8. Representations of general linear groups Appendices Index.

2,341 citations

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01 Jan 1955

Abstract: Preface to the second edition Preface to the first edition 1. On permutations 2. The definition of a group 3. On the simpler properties of a group which are independent of its mode of representation 4. Further properties of a group which are independent of its mode of representation 5. On the composition-series of a group 6. On the isomorphism of a group within itself 7. On Abelian groups 8. On groups whose orders are the powers of primes 9. On Sylow's theorem 10. On permutation-groups: transitive and intransitive groups 11. On permutation-groups: transitivity and primitivity 12. On the representation of a group of finite order as a permutation-group 13. On groups of linear substitutions 14. On the representation of a group of finite order as a group of linear substitutions 15. On group-characteristics 16. Some applications of the theory of groups of linear substitutions and of group-characteristics 17. On the invariants of groups of linear substitutions 18. On the graphical representation of a group 19. On the graphical representation of groups 20. On congruence groups Notes Index of technical terms Index of authors quoted General index.

1,172 citations

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28 Dec 1996Abstract: Part I. Calculus Of Tableux: 1. Bumping and sliding 2. Words: the plactic monoid 3. Increasing sequences: proofs of the claims 4. The Robinson-Schensted-Knuth Correspondence 5. The Littlewood-Richardson rule 6. Symmetric polynomials Part II. Representation Theory: 7. Representations of the symmetric group 8. Representations of the general linear group Part III. Geometry: 9. Flag varieties 10. Schubert varieties and polynomials Appendix A Appendix B.

1,080 citations