Abstract
THE author tells us in his preface that he found Klein's “Vorlesungen uber das Ikosaeder” and Klein and Frickes “Theorie der elliptischen Modulfunctionen” “pretty stiff reading.” Probably most students will sympathise with him and will give a ready welcome to this little book, which is intended to prepare the reader for the study of these classical treatises. The ground covered is approximately that of the last four chapters of Forsyths “Theory of Functions” (excluding automorphism), but the subect-matter is discussed in much greater detail. The first. part of the book deals with groups formed by substitutions of the form z′ = (αz + β) ÷ ; (γz + δ), especially with the five finite (polyhedral) types of group and with the infinite (modular) group in which α, β, γ, δ are integers such that αδ – βγ = 1. In the first few pages a group is defined and some of its more elementary properties proved. It must be confessed that these introductory sections are not quite satisfactory, and it is doubtful whether they would be readily intelligible to anyone who had no previous knowledge of group-theory. For instance, the author fails to make clear the distinction between a group and a semi-group, or that between an abstract group and the particular application he has in mind. The rest of part i. is, however, clear and readable, and should serve effectively the purpose intended by the author.
Funzioni poliedriche e modulari.
By G. Vivanti. Pp. viii + 437. Manuali Hoepli, 366–367. (Milano: Ulrico Hoepli, 1906.) Price 3 lire.
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Funzioni poliedriche e modulari . Nature 75, 198 (1906). https://doi.org/10.1038/075198b0
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DOI: https://doi.org/10.1038/075198b0