A Characterization of Projective Special Unitary Group U3(7)‎ by nse

Abstract EN

Let G a group and ω(G) be the set of element orders of G.

Let k∈ω(G) and let sk be the number of elements of order k in G.

Let nse(G)={sk∣k∈ω(G)}.

In Khatami et al.

and Liu's works, L3(2) and L3(4) are uniquely determined by nse(G).

In this paper, we prove that if G is a group such that nse(G) = nse(U3(7)), then G≅U3(7).