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Grunewald, Fritz J.; Segal, Daniel

The solubility of certain decision problems in arithmetic and algebra. (English) Zbl 0431.20029

Bull. Am. Math. Soc., New Ser. 1, 915-918 (1979).
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Cited in 2 Reviews
Cited in 10 Documents

MSC:

20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
11U05 Decidability (number-theoretic aspects)
16P10 Finite rings and finite-dimensional associative algebras
11E57 Classical groups
20F18 Nilpotent groups

Keywords:

decision problems; isomorphism problem for nilpotent groups; conjugacy problem
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\textit{F. J. Grunewald} and \textit{D. Segal}, Bull. Am. Math. Soc., New Ser. 1, 915--918 (1979; Zbl 0431.20029)
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References:

[1] Helmut Behr, Über die endliche Definierbarkeit verallgemeinerter Einheitengruppen, J. Reine Angew. Math. 211 (1962), 123 – 135 (German). · Zbl 0107.26202
[2] Armand Borel, Introduction aux groupes arithmétiques, Publications de l’Institut de Mathématique de l’Université de Strasbourg, XV. Actualités Scientifiques et Industrielles, No. 1341, Hermann, Paris, 1969 (French). · Zbl 0186.33202
[3] Armand Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485 – 535. · Zbl 0107.14804
[4] J. W. S. Cassels, Rational quadratic forms, London Mathematical Society Monographs, vol. 13, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1978. · Zbl 0395.10029
[5] Fritz J. Grunewald, Solution of the conjugacy problem in certain arithmetic groups, Word problems, II (Conf. on Decision Problems in Algebra, Oxford, 1976), Stud. Logic Foundations Math., vol. 95, North-Holland, Amsterdam-New York, 1980, pp. 101 – 139.
[6] Fritz J. Grunewald and Daniel Segal, A note on arithmetic groups, Bull. London Math. Soc. 10 (1978), no. 3, 297 – 302. · Zbl 0403.20030
[7] Fritz J. Grunewald and Daniel Segal, Conjugacy of subgroups in arithmetic groups, Proc. London Math. Soc. (3) 44 (1982), no. 1, 47 – 70. · Zbl 0477.20026
[8] P. Hall, Nilpotent groups, Queen Mary College, London, 1969.
[9] A. Hurwitz, Die unimodularen Substitutionen in einem algebraischen Zahlkörper, Nachr. Gesellschaft Wiss. Göttingen, 1895. · JFM 26.0224.03
[10] C. Jordan, Mémoire sur l’équivalence des formes, J. École Polytech. 48 (1880), 112-150.
[11] M. I. Kargapolov, Some questions in the theory of soluble groups, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Springer, Berlin, 1974, pp. 389 – 394. Lecture Notes in Math., Vol. 372.
[12] H. Poincaré, Sur les formes cubiques ternaires et quaternaires, J. École Polytech. 51 (1882), 45-91. · JFM 15.0097.01
[13] R. A. Sarkisjan, On the conjugacy problem, Mat. Zametkie N1 and N6, 1979. (Russian) · Zbl 0413.12014
[14] R. A. Sarkisjan, Symposium on Group Theory in Tscherkasse, Uspehi Mat. Nauk (to appear)
[15] Carl Ludwig Siegel, Zur Reduktionstheorie quadratischer Formen, Publications of the Mathematical Society of Japan, Vol. 5, The Mathematical Society of Japan, Tokyo, 1959 (German). · Zbl 0097.00901
[16] Richard G. Swan, Generators and relations for certain special linear groups, Advances in Math. 6 (1971), 1 – 77 (1971). · Zbl 0221.20060
[17] Alfred Tarski, A decision method for elementary algebra and geometry, University of California Press, Berkeley and Los Angeles, Calif., 1951. 2nd ed. · Zbl 0035.00602
[18] M. A. Taĭclin, The isomorphism problem for commutative semigroups, Mat. Sb. (N.S.) 93(135) (1974), 103 – 128, 152 (Russian).
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