On simple groups of large exponents

Abstract

It is shown that the set of pairwise non-isomorphic 2-generated simple groups of exponent n (n ≥ 2⁴⁸ and n is odd or divisible by 2⁹ ) is of cardinality continuum. As a corollary, for any sufficiently large n the set of pairwise non-isomorphic 2-generated groups of exponent n is of cardinality continuum.