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The 1-, 2-, and 3-characters determine a group
Author(s):
H.
-J.
Hoehnke;
K.
W.
Johnson
Journal:
Bull. Amer. Math. Soc.
27
(1992),
243-245.
MSC (1991):
Primary 15A15, 16A26, 16H05, 16K20, 16S99, 20B05, 20B40, 20C15
MathSciNet review:
1149873
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References |
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Additional information
References:
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- H. Brandt, Idealtheorie in Quaternionenalgebren, Math. Ann. \textbf{99} (1928), 1--29. MR 1512436
- [Bo]
- N. Bourbaki, Alg\`ebre. {\rm I}, Paris, 1970. MR
- [Br]
- R. Brauer, Representations of finite groups, Lectures in Modern Mathematics {\rm (T. L. Saaty, ed.)}, Wileÿ, 19øÄ63, pp.~133--175. MR 178056
- [FS]
- E. Formanek and D. Sibley, The group determinant determines the group, Proc. Amer. Math. Soc. {\bf 112} (1991), 649--656. MR 1062831
- [Fr1]
- G. Frobenius, \"Uber die Primfaktoren der Gruppendeterminante, S'ber. Akad. Wiss. Berlin (1896), 1343--1382. MR
- [Fr2]
- G. Frobenius, \"Uber die Darstellung der endlichen Gruppen durch lineare Substitutionen, S'ber. Akad. Wiss. Berlin (1898), 944--1015. MR
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- T. Hawkins, The origins of the theory of group characters, Arch. Hist. Exact Sci. \textbf{7} (1971), 142--170. MR 1554141
- [Ha2]
- T. Hawkins, New light on Frobenius' creation of the theory of group characters, Arch. Hist. Exact Sci. \textbf{12} (1974), 217--243. MR 446837
- [Ho1]
- H.-J. Hoehnke, \"Uber komponierbare Formen und konkordante hyperkomplexe Gr\"ossen, Math. Z. \textbf{70} (1958), 1--12. MR 99353
- [Ho2]
- H.-J. Hoehnke, \"Uber Beziehungen zwischen Problemen von H. Brandt aus der Theorie der Algebren und den Automorphismen der Normenform, Math. Nachr. \textbf{34} (1967), 229--255. MR 218392
- [J]
- K. W. Johnson, On the group determinant, Math. Proc. Cambridge Philos. Soc. \textbf{109} (1991), 299--311. MR 1085397
- [JS]
- K. W. Johnson and Surinder Sehgal, The {\rm 2}-character table does not determine a group, {\rm preprint}. MR 1166358
- [Ro]
- M. Roitman, A complete set of invariants for finite groups, Adv. in Math. \textbf{41} (1981), 301--311. MR 630923
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15A15, 16A26, 16H05, 16K20, 16S99, 20B05, 20B40, 20C15
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15A15, 16A26, 16H05, 16K20, 16S99, 20B05, 20B40, 20C15
Additional Information:
DOI:
10.1090/S0273-0979-1992-00302-6
PII:
S 0273-0979(1992)00302-6
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