A CHARACTERIZATION OF A5 BY ITS AVERAGE ORDER

Let o(G) be the average order of a finite group G. M. Herzog, P. Longobardi and M. Maj [M. Herzog, P. Longobardi and M. Maj, Another criterion for solvability of finite groups, J. Algebra, 597 (2022) 1-23.] showed that if G is non-solvable and o(G) = o(A5), then G ∼= A5. In this note, we prove that the equality o(G) = o(A5) does not hold for any finite solvable group G. Consequently, up to isomorphism, A5 is determined by its average order.