Free Algebraic Structures
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Home > Art, Film & Photography > Free Algebraic Structures: Free Group, Free Abelian Group, Free Object, Trace Monoid, History Monoid, Free Boolean Algebra, Free Lattice
Free Algebraic Structures: Free Group, Free Abelian Group, Free Object, Trace Monoid, History Monoid, Free Boolean Algebra, Free Lattice

Free Algebraic Structures: Free Group, Free Abelian Group, Free Object, Trace Monoid, History Monoid, Free Boolean Algebra, Free Lattice


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About the Book

Chapters: Free Group, Free Abelian Group, Free Object, Trace Monoid, History Monoid, Free Boolean Algebra, Free Lattice, Free Monoid, Free Module, Free Lie Algebra, Free Algebra, Stably Free Module, Free Partially Commutative Group. Source: Wikipedia. Pages: 64. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st = su ut ). A related but different notion is a free abelian group. Free groups first arose in the study of hyperbolic geometry, as examples of Fuchsian groups (discrete groups acting by isometries on the hyperbolic plane). In an 1882 paper, Walther von Dyck pointed out that these groups have the simplest possible presentations. The algebraic study of free groups was initiated by Jakob Nielsen in 1924, who gave them their name and established many of their basic properties. Max Dehn realized the connection with topology, and obtained the first proof of the full Nielsen-Schreier Theorem. Otto Schreier published an algebraic proof of this result in 1927, and Kurt Reidemeister included a comprehensive treatment of free groups in his 1932 book on combinatorial topology. Later on in the 1930s, Wilhelm Magnus discovered the connection between the lower central series of free groups and free Lie algebras. The group (Z, +) of integers is free; we can take S = {1}. A free group on a two-element set S occurs in the proof of the BanachTarski paradox and is described there. On the other hand, any nontrivial finite group cannot be free, since the elements of a free generating set of a free group have infinite order. In algebraic topology, the fundamental group of...More: http: //booksllc.net/?id=597


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Product Details
  • ISBN-13: 9781155197708
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 66
  • Spine Width: 4 mm
  • Weight: 109 gr
  • ISBN-10: 1155197704
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Free Group, Free Abelian Group, Free Object, Trace Monoid, History Monoid, Free Boolean Algebra, Free Lattice
  • Width: 229 mm


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