(adsbygoogle = window.adsbygoogle || []).push({}); NEED HELP!!! with permutation proof

Sorry for any confusion the question I have is:

Show that a permutation with odd order must be an even permutation.

The order of a permutation of a finite set written in disjoint cycle form

is the least common multiple of the lengths of the cycles.

This is what I have worked out so far:

Lete= epsilon

LetB= a permutation

Letk= any integer

Now sayB^(2k+1) = e. WhereB^(2k+1)is an odd permutation.

ThenB^(2k)= B^(-1).

ButB^(2k) = B^(k)^2is even.

I would really appreciate some help in putting this

proof together in a more coherent fashion.

I am very confused. Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Clarification of Permuatation Question

**Physics Forums | Science Articles, Homework Help, Discussion**