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This article is cited in 1 scientific paper (total in 1 paper)
On the word problem and the conjugacy problem for groups of the form $F/V(R)$
M. I. Anokhin M. V. Lomonosov Moscow State University
Abstract:
Let $F$ be a free group with at most countable system $\mathfrak x$ of free generators, let $R$ be its normal subgroup recursively enumerable with respect to $\mathfrak x$, and let $\mathfrak V$ be a variety of groups that differs from $\mathfrak O$ and for which the corresponding verbal subgroup $V$ of the free group of countable rank is recursive. It is proved that the word problem in $F/V(R)$ is solvable if and only if this problem is solvable in $F/R$, and if $|\mathfrak x|\ge3$, then there exists an $R$ such, that the conjugacy problem in $F/R$ is solvable, but this problem is unsolvable in $F/V(R)$ for any Abelian variety $\mathfrak V\ne\mathfrak E$ (all algorithmic problems are regarded with respect to the images of $\mathfrak x$ under the corresponding natural epimorphisms).
Received: 13.05.1994
Citation:
M. I. Anokhin, “On the word problem and the conjugacy problem for groups of the form $F/V(R)$”, Mat. Zametki, 61:1 (1997), 3–9; Math. Notes, 61:1 (1997), 3–8
Linking options:
https://www.mathnet.ru/eng/mzm1476https://doi.org/10.4213/mzm1476 https://www.mathnet.ru/eng/mzm/v61/i1/p3
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