Concerning Abelian-regular transitive triple systems. (English) JFM 29.0120.01

Verf. beschäftigt sich im Anschluss an die Arbeiten von Netto (Math. Ann. 42, 143-152, 1893), Heffter (Math. Ann. 49, 101-112 1897) und von ihm selbst (Math. Ann. 43, 271-285, 1893) mit solchen Tripelsystemen, deren zugehörige Substitutionsgruppe transitiv ist und eine reguläre Abel’sche Untergruppe enthält, deren Ordnung gleich ihrem Grade ist. Die ausführlichere Angabe der Resultate setzt indessen so viele Erklärungen voraus, dass auf die Abhandlung selbst verwiesen werden muss.


20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)
20B99 Permutation groups
20K99 Abelian groups


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[1] Netto, Zur Theorie der Tripelsysteme (Mathematische Annalen, vol. 42, pp. 143-152, 1893). · JFM 25.0197.04
[2] Heffter,Ueber Tripelsysteme (Mathem. Ann., vol. 49, pp. 101-112, 1897). · JFM 28.0128.02
[3] Weber, Algebra, vol. 2, p. 39 fg.
[4] I use thegeneral matrix notation for configurations introduced in I (The General Tactical Configuration: Definition and Notation), of my paperTactical Memoranda I?III (American Journal of Mathematics, vol. 18, pp. 264-303, 1896).
[5] Cf.Mathem. Annalen, vol. 43, p. 272.
[6] Concerning Triple Systems, (Mathem. Annalen), vol. 43, pp. 271-285, 1893). · JFM 25.0198.02
[7] Galois,Sur la théorie des nombres (Bulletin des Sciences Mathématiques de M. Ferussac, vol. 13, p. 428, 1830; reprinted,Journal de Mathematiques pures et appliquées, vol. 11, pp. 398-407, 1846).
[8] Serret,Algèbre supérieure, fifth edition, vol. 2, pp. 122-189.
[9] Jordan,Traité des substitutions, pp., 14-18.
[10] Moore,A doubly infinite system of simple groups (Mathematical Papers read at the... Congres...Chicago 1893, pp. 208-242, 1896; in abstract,Bulletin of the New York Mathematical Society, vol. 3, Dec., 1893. § 3 is an abstract ormul ation of the Galois field theory). · JFM 25.0198.01
[11] Dirichlet-Dedekind,Zahlentheorie, fourth edition, § 128.
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