Consider the following statements : S (G, *) a ∈ G

1 : If a group is of order n, and is am = e m ≤ n such that for some integer , then m must divide n. S (G, *)

2 : If a group is of even order, then there a ∈ G a ≠ e must be an element such that and a * a = e . Which of the statements is (are) correct? S

1. AOnly 1 S
2. BOnly 2 S S
3. CBoth 1 and 2 S S
4. DNeither 1 nor 2

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: C. Both 1 and 2 S S

Explanation

By Lagrange, the order of an element divides the group order (S1, as intended). A group of even order has an element of order 2 (Cauchy), i.e. a ≠ e with a * a = e (S2). Both correct.