Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Permutation Groups
Replies: 13   Last Post: Feb 2, 2004 2:54 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Chuck Cadman

Posts: 16
Registered: 12/12/04
Re: Permutation Groups
Posted: Oct 10, 1999 11:42 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply




Jack Patel wrote in message ...
>I understand the theory of Permutaion Groups very well and understand
>the concept of an alternating subgroup of degree n.
>
>However, I am stumped on these types of questions:
>
>1) How many elements of order 5 are in S7? (S=Symmetric Group)
>2) How many odd permutations of order 4 does S6 have?
>3) How many elements of order 5 are there in A6? (A=Alternating)
>4) What is the maximum order of any element in A10? (I think 21 ?)
>
>I especially would like to know how to do number 1 because it is a
>very basic problem.


Given the fact that any permutation can be expressed as a product of
disjoint cycles, it's easy to show that the only elements of order 5 are
5-cycles (since 5 is prime). So you just need to count the number of ways
that you can choose 5 distinct numbers between 1 and 7 and multiply by the
number of unique 5-cycles that you can obtain from any such collection. I
think it's 7!/10.

Chuck Cadman








Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.