A group determinant determines its group
HTML articles powered by AMS MathViewer
- by Richard Mansfield PDF
- Proc. Amer. Math. Soc. 116 (1992), 939-941 Request permission
Abstract:
The determinant of a group’s multiplication table determines the group.References
- Nicolas Bourbaki, Algebra I. Chapters 1–3, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1998. Translated from the French; Reprint of the 1989 English translation [ MR0979982 (90d:00002)]. MR 1727844
- Edward Formanek and David Sibley, The group determinant determines the group, Proc. Amer. Math. Soc. 112 (1991), no. 3, 649–656. MR 1062831, DOI 10.1090/S0002-9939-1991-1062831-1 F. G. Frobenius, Über die Darstellung der endlichen Gruppen durch lineare substitionen, Sitz. Kon. Preuss. Akad. Wiss. Berlin (1897), 944-1015; F. G. Frobenius—Gessamelte Abhandlung, vol. III, Springer-Verlag, Berlin, 1968. H.-J. Hoenke and K. W. Johnson, The $3$-characters are sufficient for the group determinant, preprint.
- Hans-Jürgen Hoehnke, Über komponierbare Formen und konkordante hyperkomplexe Grössen, Math. Z. 70 (1958), 1–12 (German). MR 99353, DOI 10.1007/BF01558573
- Hans-Jürgen Hoehnke, Über Beziehungen zwischen Problemen von H. Brandt aus der Theorie der Algebren und den Automorphismen der Normenform, Math. Nachr. 34 (1967), 229–255 (German). MR 218392, DOI 10.1002/mana.19670340115
- K. W. Johnson, Latin square determinants, Algebraic, extremal and metric combinatorics, 1986 (Montreal, PQ, 1986) London Math. Soc. Lecture Note Ser., vol. 131, Cambridge Univ. Press, Cambridge, 1988, pp. 146–154. MR 1052664
- K. W. Johnson, Latin square determinants. II, Discrete Math. 105 (1992), no. 1-3, 111–130. MR 1180197, DOI 10.1016/0012-365X(92)90136-4
- Moshe Roitman, A complete set of invariants for finite groups and other results, Adv. in Math. 41 (1981), no. 3, 301–311. MR 630923, DOI 10.1016/0001-8708(81)90023-2
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 939-941
- MSC: Primary 20C15; Secondary 15A15, 16H05, 16K20
- DOI: https://doi.org/10.1090/S0002-9939-1992-1123661-6
- MathSciNet review: 1123661