This article is cited in 3 scientific papers (total in 3 papers)
Some relations between the word and divisibility problems in groups and semigroups
O. A. Sarkisyan
This paper studies the relationship between the word problems in a finitely presented semigroup $\Pi$, which is embeddable in a group, and in the group $\Gamma$ with the same generators and defining relations. We construct an example showing that even in the case when not only the word problem but also the left and right divisibility problems are solvable in $\Pi$, the word problem in $\Gamma$ may be unsolvable. Furthermore, we prove that the additional condition of the absence of cycles in the system of defining relations of $\Pi$ issufficient for the solvability of its word and divisibility problems to imply the solvability of the word problem in $\Gamma$.
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Mathematics of the USSR-Izvestiya, 1980, 15:1, 161–171
MSC: 20F10, 20M05
O. A. Sarkisyan, “Some relations between the word and divisibility problems in groups and semigroups”, Izv. Akad. Nauk SSSR Ser. Mat., 43:4 (1979), 909–921; Math. USSR-Izv., 15:1 (1980), 161–171
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\paper Some relations between the word and divisibility problems in groups and semigroups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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This publication is cited in the following articles:
O. A. Sarkisyan, “On the word and divisibility problems in semigroups and groups without cycles”, Math. USSR-Izv., 19:3 (1982), 643–656
V. S. Guba, “On the relationship between the problems of equality and divisibility of words for semigroups with a single defining relation”, Izv. Math., 61:6 (1997), 1137–1169
S. I. Adian, V. G. Durnev, “Decision problems for groups and semigroups”, Russian Math. Surveys, 55:2 (2000), 207–296
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