Question

Every group of order 7 is

• A. not abelian
• B. not cyclic
• C. cyclic
• D. None of these

Hint:

Every group of prime order is cyclic and abelian. This is a key theorem in abstract algebra — memorise it for exams.

Answer 1

The Correct Option is C

Step 1: Conceptual Understanding:
A fundamental result in group theory states that every group whose order is a prime number must be cyclic.
Step 2: Explanation in Detail:
The number 7 is prime. By Lagrange's theorem and the corollary for prime-order groups, every group of prime order $p$ is cyclic (generated by any non-identity element) and therefore also abelian.
Step 3: Therefore, Stating the Final Answer
Every group of order 7 is cyclic (and hence abelian).