On simple groups of large exponents

• Date: 2018
• Main Author: Sonkin, Dmitriy
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Burnside group; van Kampen diagram; graded diagram; graded presentation; non-isomorphic 2-generated torsion simple groups; 20F50; 20F05; 20F06
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1013
• Journal Title: Algebra and Discrete Mathematics

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 e...