Question

Identify the false statement

• A. A non-empty subset $H$ of a group $G$ is a subgroup of $G$ if and only if for every $a, b \in H \Rightarrow a * b^{-1} \in H$
• B. The intersection of two subgroups of a group $G$ is again a subgroup.
• C. A group of order three is not a belian.
• D. If in a group $G,(ab)^2 = a^2b^2 \forall a, b \in G$, then $G$ is abelian

Answer 1

Answer: (C)

A group of order three is not a belian.

Answer 2

A group of order three is not abelian is not true.
If $O(G)$ = prime, then G is always abelian and $O(G) \leq 6$ always abelian group.