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Some recognizable properties of solvable groups. (English) Zbl 0455.20027


MSC:

20F16 Solvable groups, supersolvable groups
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
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References:

[1] Adian, S.I.: Algorithmic unsolvability of problems of recognition of certain properties of groups. Dokl. Akad. Nauk SSSR (N.S.)103, 533-535 (1955) [russian]
[2] Adian, S.I.: Unsolvability of some algorithmic problems in the theory of groups. Trudy Moskov. Math. Ob??.6, 231-298 (1957) [russian]
[3] Baumslag, G., Cannonito, F.B., Miller, III, C.F.: Infinitely generated subgroups of finitely presented groups I. Math. Z.153, 117-134 (1977) · Zbl 0337.20016 · doi:10.1007/BF01179785
[4] Baumslag, G., Cannonito, F.B., Miller, III, C.F.: Computable algebra and groups embeddings. J. Algebra 1981, in press · Zbl 0497.20023
[5] Cannonito, F.B.: Two decidable Markov properties over a class of groups. Algebra i Logika (1980, in press) · Zbl 0452.20024
[6] Noskov, G.A., Remeslennikov, V.N., Romankov, V.A.: Infinite groups. In: Results in science and technology17. Moscow 1979 [russian]
[7] Remeslennikov, V.N., Romanovskii, N.S.: Algorithmic problems for solvable groups. In: Word problems II. The Oxford Book (eds. Adian, Boone, Higman), pp. 337-346. Amsterdam-New York-Oxford: North Holland 1980
[8] Rabin, M.O.: Recursive unsolvability of group theoretic problems. Ann. of Math. (2)67, 172-194 (1958) · Zbl 0079.24802 · doi:10.2307/1969933
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