A NEW CHARACTERIZATION OF SPORADIC HIGMAN-SIMS AND HELD GROUPS

Let G be a group and omega(G) be the set of element orders of G. Let k is an element of omega(G) and s(k) be the number of elements of order k in G. Let nse( G) = {s(k)vertical bar k is an element of omega (G)}. The projective special linear groups L-3(4) and L-3(5) are uniquely determined by nse. In this paper, we prove that if G is a group such that nse(G)= nse(M) where M is a sporadic Higman-Sims or Held group, then G congruent to M.