If every element of a group G is its own inverse then G is called?

Maths / Basic Math — Multiple-choice practice

A. None of these
B. Cyclic
C. Abelian
D. Finite

Correct answer

Abelian

Explanation

Explanation If every element of a group G G is its own inverse, then g 2 = e g^2 = e for all g ∈ G g in G , meaning all elements are of order 2. Such a group is Abelian because the group operation commutes: ( g h ) 2 = e (gh)^2 = e implies g g and h h must commute.

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If every element of a group G is its own inverse then G is called?

Correct answer

Explanation

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