• Support PF! Buy your school textbooks, materials and every day products Here!

Abstract Algebra - Cyclic groups

  • Thread starter basketm19
  • Start date
  • #1
3
0
(This is my first post on PF btw - I posted on this another thread, but I'm not sure if I was supposed to)

I was doing some practice problems for my exam next week and I could not figure this out.

Homework Statement



Suppose a is a group element such that |a^28| = 10 and |a^22| = 20. Determine |a|.

Homework Equations



Let a be element of order n in group and let k be a positive integer. Then <a^k> = <a^gcd(n,k)> and |a^k| = n/gcd(n,k).

The Attempt at a Solution



10 = n/gcd(n, 28); 20 = n/gcd(n, 22)

Setting n equal to each other, 10gcd(n, 28) = 20gcd(n,22)

gcd(n, 28) = 2gcd(n, 22)

The possible values for n are 4, 8, 12, 16, 20, 24, ... , so on.

Not sure where to go from here.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

Related Threads on Abstract Algebra - Cyclic groups

Replies
4
Views
2K
  • Last Post
Replies
4
Views
3K
Replies
1
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
10
Views
3K
Replies
2
Views
759
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
1
Views
1K
Top