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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,
Die einfachen Gruppen im erasten und zweiten Hundert der Ordnungszahlen.
Leipzig, B.G. Teubner, 1892 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. XL. [40]. Band. 1. Heft."" Entire issue offered. Internally very fine and clean. [Hölder:] Pp. 55-88. [Entire issue: Pp. 1-156].
First printing of Hölder's paper on group theory. ""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)The issue also contains: 1. Klein, Felix. Ueber den Hermite'schen Fall der Lame'schen Differentialgleichung. Pp. 125-29.2. Klein, Felix. Ueber den Begriff des functionentheoretischen Fundamentalbereichs. Pp. 130-39.
Anschauung und Denken in der Geometrie. Akademische Antrittsvorlesung gehalten am 22. Juli 1899. Mit Zusätzen, Anmerkungen und einem Register.
Leipzig, B.G. Teubner, 1900. Hcloth with gilt lettering to spine. Stamps to foot of titlepage and on last page. 6 margins with contemp. annotations, otherwise clean. (2),75 pp.
First edition of Hölder's inaugural lecture when he succeeded Sophus Lie in Leipzig.
