On simple groups of large exponents

Abstract

It is shown that the set of pairwise non-isomorphic \(2\)-generated simple groups of exponent \(n\) (\(n \ge 2^{48}\) and \(n\) is odd or divisible by \(2^9\)) 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.