Question

If an abelian group G is simple then possible order of G is what ? ​

Answer 1

Answer:

prime

Step-by-step explanation:

If G is a simple abelian group, then the order of G is prime. Suppose that G is a simple abelian group. Then G is a nontrivial group by definition. We first show that G is a finite group.

Answer 2

G's order is prime when it's a simple abelian group.

• If there are only the trivial group or G as normal subgroups, a nontrivial group is called simple.
• A prime order cyclic group is any simple Abelian group.
• Because all Abelian groups have normal subgroups and all cyclic groups are Abelian, the only simple cyclic groups are those with no subgroups other than trivial and improper subgroups that encompass the entire original group.