HÖLDER, OTTO.

Bildung zusammengesetzter Gruppen.

Leipzig, B. G. Teubner, 1895. 8vo. In the original printed wrappers. In "Mathematische Annalen, Begründet 1868 durch Alfred Clebsch und Carl Neumann", 46. band, 3 heft. Entire heft 3 offered. No backstrip and a small tear to back wrapper, otherwise fine and clean. Pp. 321-422. [Entire heft: Pp. 321-480].

First printing of Hölder's extensive and important paper on symmetric groups.

Hölder owed his interest in group theory and Galois theory primarily to Kronecker, but also to Felix Klein, in whose seminar at Leipzig Hölder participated soon after receiving his doctorate.
Hölder turned his attention first to simple groups. Besides the simple groups of orders 60 and 168 already known at the time, he found no new ones with a composite order less than 200. Nevertheless, he considered his method to be "of some interest so long as we do not possess a better one suitable for handling the problem generally." Such a general method is still lacking, despite the progress and great efforts of recent years. (DSB).

He is famous for many things including: Hölder's inequality, the Jordan-Hölder theorem, the theorem stating that every linearly ordered group that satisfies an Archimedean property is isomorphic to a subgroup of the additive group of real numbers,

Order-nr.: 49761