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]).