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The present article used the classification of simple groups to prove that group G is isomorphic to the projective linear group PGL(2, p) if |G|= p(p2−1) and p2−1 ∈ N(G), where N(G) is the collection of conjugacy class length of G and p is a prime.

Re-characterization of PGL(2, p) by its order and one class length