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Concerning the general equations of the seventh and eighth degrees

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Literatur

  1. There is contact here with my papers:Concerning Jordan's Linear Groups (Bulletin of the American Mathematical Society, vol. 2, pp. 33–43, 1895),Tactical Memoranda I–III (American Journal of Mathematics, vol. 18, 264–303, 1896).

  2. It is to be noted that in introducing the notion of the group of isomorphisms of a group (loc. cit.,Concerning Jordan's Linear Groups (Bulletin of the American Mathematical Society, vol. 2, pp. 223, 1895), and especially in applying it in connection with the Abelian group of orderp n and type (111... ton units) to the study of the linear groups (loc. cit.:Concerning Jordan's Linear Groups (Bulletin of the American Mathematical Society, vol. 2, pp. 336–339, 342, 1895) Burnside should have cited my papers:The Group of Holoedric Transformation into Itself of a given Group, andConcerning Jordan's Linear Groups (Bulletin of the American Mathematical Society, vol. 1, pp. 61–66, 1894, and vol. 2, pp. 33–43, 1895). Cf. the foot-note near the close of §1 of the present paper.

  3. This well-known doubling process first occurs in a paper by Horner:On Triads of Once-Paired Elements (Quarterly Journal of Mathematics, vol. 9, pp. 15–18, 1868). He speaks however explicitly only of triple systems which may be arranged “in ascending order” (loc. cit.,Concerning Jordan's Linear Groups (Bulletin of the American Mathematical Society, vol. 2, p. 15, 1895).

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  4. Moore:Concerning the Abstract Group... (loc. cit.,Concerning Jordan's Linear Groups (Bulletin of the American Mathematical Society, vol. 2, pp 33–43, 1895, theorems B and C).

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    Eliakim Hastings Moore

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Presented to the Chicago Section of the American Mathematical Society, Dec. 31, 1897, and later slightly enlarged.

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Moore, E.H. Concerning the general equations of the seventh and eighth degrees. Math. Ann. 51, 417–444 (1898). https://doi.org/10.1007/BF01446471

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