Processing math: 100%
Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: permutation group

Bottom of Page

1 to 9 of 9

  1.  

  1. Some minimal content, and a couple of examples.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 31st 2018

    added the line:

    “Hence these are the subgroups of symmetric groups.”

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 31st 2018

    oh, sorry, now I see that this is stated later as the definition. Hm, maybe it’s still worthwhile to say it right away in the Idea-section, too.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 31st 2018

    Do rotation permutations form a group, as it seems to suggest here?

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 31st 2018

    Re rotation permutation: yes, they form a group because it’s just transporting the structure of the group ℤn↪Aut({1,…,n}) across the given bijection i on which the definition depends. But the language “rotation permutation of X” could easily invite confusion since it suppresses mention of this i which is actually crucial. Clearly rotations relative to different i’s do not compose.

    At first the article had the title cyclic permutation which could be defined as a transitive ℤ-set structure on X: σ:ℤ→Aut(X) (normally considered given as σ(1); also this definition allows the case where X to be countably infinite, although usually one would constrain to X finite). That would be the notion of rotation permutation but untethered to a particular i.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 31st 2018
    • (edited Dec 31st 2018)

    Yes, the cyclic group.

    [edit: ah, overlapped with Todd]

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 31st 2018

    Isn’t the wording misleading at rotation permutation?

    A rotation permutation is, roughly speaking, a permutation in which, if we view the elements of a finite set as people standing in a circle, everybody shifts one step to the right, or everybody shifts one step to the left.

    This sounds to me like a generator.

  8. Thanks David, fixed now.

  9. Also attempted to improve the rotation permutations example according to Todd’s remarks (thanks!).

1 to 9 of 9

  1.