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RESEARCH ARTICLE

On simple groups of large exponents

Dmitriy Sonkin

Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA

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.

Keywords: Burnside group, van Kampen diagram, graded diagram, graded presentation, non-isomorphic $2$-generated torsion simple groups.

MSC: 20F50, 20F05, 20F06

Received: 12.06.2004
Revised: 15.12.2004

Language: English

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