Thread: Finding the cyclic subgroup...

Find the cyclic subgroup generated by
2 1
0 2
(matrix)
in .

I suppose im confused as to what exactly it's asking me to do.
signifies 2x2 matrices with mod3 entried, correct? How do I find the cyclic subgroup?

Originally Posted by elninio

Find the cyclic subgroup generated by
2 1
0 2
(matrix)
in .

I suppose im confused as to what exactly it's asking me to do.
signifies 2x2 matrices with mod3 entried, correct? How do I find the cyclic subgroup?

The cyclic subgroup generated by the element is all elements of the form for . So, just find , , , etc until you get back to the identity. The powers of your generator will be your group.

Thank you! I've found the answer. Its too long to write out but it contains six matrices.

Originally Posted by elninio

Thank you! I've found the answer. Its too long to write out but it contains six matrices.

Correct.

Tonio