elements of A5

## Primary tabs

# elements of A5

Submitted by crazziqt467 on Tue, 12/02/2008 - 09:33

Forums:

how does one determine how many elements of a certain order there are in A5 the even permutation group? thanks!

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections

## Versions

(v1) by crazziqt467 2008-12-02

## Re: elements of A5

Here is the strategy to find, the number of subgroups of a given order say [;m;] of [;A_n;]. I do not know whether there is a closed form, but the following can be implemented as a algorithm on the computer.

1. First verify the possibility by writing down a cycle structure (disjoint cycles)for such an operation. Remember that [;lcm;] of the lengths of the cycles should give [;m;] and the number of transpositions should be even.

2. Taking care of possible automorphisms, we can map every element in a cycle to another element, thus a stirling number with certain correction.