Answer to Question #203259 in Abstract Algebra for Anand

Question

Give the smallest n ∈ N for which An is non-abelian. Justify your answer.

Answer 1

Solution:

$A_5$  is the smallest non-abelian simple group, having order 60, and the smallest non-solvable group. Because we know that the group A_n is abelian if and only if n ≤ 4.