Unsolvability of the endomorphic reducibility problem in free nilpotent groups and in free rings. (English. Russian original) Zbl 0411.20021
Algebra Logic 16, 310-320 (1978); translation from Algebra Logika 16, 457-471 (1977).
MSC:
| 20F10 | Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) |
| 20F18 | Nilpotent groups |
| 20E36 | Automorphisms of infinite groups |
| 20F16 | Solvable groups, supersolvable groups |
| 16S10 | Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) |
| 16W20 | Automorphisms and endomorphisms |
| 16N40 | Nil and nilpotent radicals, sets, ideals, associative rings |
| 17A50 | Free nonassociative algebras |
| 17B30 | Solvable, nilpotent (super)algebras |
References:
| [1] | R. C. Lyndon, ”Dependence in groups,” Colloq. Math.,14, 275–283 (1966). · Zbl 0141.02102 |
| [2] | G. Baumslag, W. W. Boone, and B. H. Neumann, ”Some unsolvable problems about elements and subgroups of groups,” Math. Scand.,7, No. 1, 191–201 (1959). · Zbl 0104.00704 |
| [3] | Yu. V. Matiyasevich, ”Enumerable sets are Diophantine,” Dokl. Akad. Nauk SSSR,191, No. 2, 279–282 (1970). · Zbl 0212.33401 |
| [4] | M. I. Kargapolov and Yu. I. Merzlyakov, Foundations of Group Theory [in Russian], Nauka (1972). · Zbl 0499.20001 |
| [5] | M. I. Kargapolov, V. N. Remeslennikov, N. S. Romanovskii, V. A. Roman’kov, and V. A. Churkin, ”Algorithmic question for{\(\sigma\)}-power groups,” Algebra Logika,8, No. 6, 643–659 (1969). |
| [6] | M. Hall, Jr., The Theory of Groups, Macmillan, New York (1959). |
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