143k views
0 votes
We consider the group Z₅₃. What are the possible element orders? How many elements exist for each order?

1 Answer

3 votes

Final answer:

In the group Z₅₃, the possible element orders are 1, 2, 5, and 53. The number of elements for each order is 1 element of order 1, 1 element of order 2, 4 elements of order 5, and 52 elements of order 53.

Step-by-step explanation:

In the group Z₅₃, the possible element orders are 1, 2, 5, 53.

The number of elements for each order can be determined using a property of cyclic groups. In a cyclic group of order n, there is exactly one element of order d for every divisor d of n. Therefore, for the group Z₅₃, there is 1 element of order 1, 1 element of order 2, 4 elements of order 5, and 52 elements of order 53.

User Cmrn
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.