Transposition (group theory)

From Maths
Jump to: navigation, search
Stub grade: A*
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Routine for first years, needed for some manifolds work.
  • Demote to grade D once more content is added


Let [ilmath]S_k[/ilmath] denote the symmetric group on [ilmath]k\in\mathbb{N} [/ilmath] symbols. Then:

  • [ilmath](i j)[/ilmath] denotes (in ordinary cycle notation the permutation:
    • [ilmath](i j): i\mapsto j[/ilmath], [ilmath](i j):j\mapsto i[/ilmath] and for all other [ilmath]m\in\{1,\ldots,k\} [/ilmath] (so [ilmath]m\ne i[/ilmath] and [ilmath]m\ne j[/ilmath]) we have: [ilmath](i j):m\mapsto m[/ilmath]

Such an [ilmath](i j)[/ilmath] is called a transposition.

See also