Mathematics · Group Theory

Which of the following statements are correct regarding the classification and properties of groups? A. A binary structure is classified as a group if it satisfies associativity, contains an identity element, and has an inverse for every element. B. A group is classified as an abelian group if the operation satisfies a * b = b * a for all elements in the group. C. The inverse of a given element within a group structure is not uniquely determined. D. A non-empty subset of a group forms a subgroup if it contains the identity, is closed under the operation, and contains the inverse for each of its elements. Choose the most appropriate answer from the options given below: