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ON THE (2,3)-GENERATION OF AUTOMORPHISM GROUPS OF FREE GROUPS

Published online by Cambridge University Press:  01 January 1997

M. CHIARA TAMBURINI  and
JOHN S. WILSON
M. CHIARA TAMBURINI
Affiliation:
Università Cattolica del Sacro Cuore, Via Trieste 17, 25121 Brescia, Italy
JOHN S. WILSON
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham B15 2TT
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Abstract

A group is said to be (2,3)-generated if it can be generated by an element of order 2 and an element of order 3. The class of (2,3)-generated groups seems to be rather extensive. From results of Schupp [7] and Mason and Pride [3], it is known that there are 2ℵ0 isomorphism classes of (2,3)-generated groups, and moreover that every countable group can be embedded in a (2,3)-generated group. All finite non-abelian simple groups are (2,3)-generated, with the exception of some groups of low rank in characteristics 2 and 3 (see Wilson [13] or Sanchini and Tamburini [6]).

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 1 , January 1997 , pp. 43 - 48
Copyright
© The London Mathematical Society 1997

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