Talk:Permutation group

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[edit] Examples of permutation groups

I added two examples from my own work. Others may argue that this is too egocentric. Cullinane 21:54, 10 August 2005 (UTC)

[edit] Permutations of infinite sets?

I would be interested to know about permutations (and permutation groups) of infinite sets (eg: Z or Q). The article says that "if M is any finite or infinite set, then the group of all permutations of M is often written as Sym(M)". I'm interested to know how a permutation would be defined for an uncountable set like R.

If you know anything about this topic please include some information here (or start another article about it).

Sorry, forgot to sign that last commentDonkeyKong the mathematician (in training) 06:48, 28 May 2006 (UTC)
A permutation of M may be defined as a bijection of M into itself (an automorphism in the category of sets), thus S(M) is the set of all such permutations for a given set M. Of course one cannot "explicitely" write the correspondence table
    [  x1     x2    ... ]
f = [                   ]
    [ f(x1)  f(x2)  ... ]
of such a permutation, if it has an infinite support; however, this is possible if it has a finite support (supp f = { x | f(x) <> x }), in which case one would only write the elements on which it acts nontrivially. In that case, one can also decompose it into cycles and define its order etc. in the usual manner. It's easy to see that the subset So(M) = { f &in; S(M) | suppf is finite } is a (normal) subgroup of S(M). — MFH:Talk 03:02, 11 November 2006 (UTC)

[edit] Inversions and transpositions

{NOTE that the permutation 4,3,1,2 has five inversions but only three transpositions. There is an error in the text} —Preceding unsigned comment added by 01001 (talk • contribs)