J. Birman has raised the question as to whether every element of the mapping class group (the Teichmüller modular group) is in the nonnalizer of some element of finite order. In this paper elements of the mapping class group which are not in the normalizer of any element of finite order are constructed. J. Birman has raised the question as to whether every element of the mapping class group of genus g, M(g), is in the normalizer of some element of finite order (see p. 190 and p. 219, problem 26

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... of [1]). In this paper we find an element of M(g), g > 3, which is not in the normalizer of any element of finite order. The example is found by combining the methods of Raymond and Tollefson [3] with a result about the action on homology of automorphisms of a surface [2] . I want to thank J. Birman for pointing out the relevance of [3] .