2016
DOI: 10.1090/tran/6880
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Magnus embedding and algorithmic properties of groups 𝐹/𝑁^{(𝑑)}

Abstract: Abstract. In this paper we further study properties of Magnus embedding, give a precise reducibility diagram for Dehn problems in groups of the form F/N (d) , and provide a detailed answer to Problem 12.98 in Kourovka notebook. We also show that most of the reductions are polynomial time reductions and can be used in practical computation.

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Cited by 4 publications
(5 citation statements)
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“…We replace each of these formulas by an equivalent exponent equation over BS (1,2). For this we use the two generators a and t as in Equation (15). The formula x + y = z is clearly equivalent to a x a y = a z , i.e., a x a y a −z = 1.…”
Section: E Exponent Equations In Baumslag-solitar Groupsmentioning
confidence: 99%
See 1 more Smart Citation
“…We replace each of these formulas by an equivalent exponent equation over BS (1,2). For this we use the two generators a and t as in Equation (15). The formula x + y = z is clearly equivalent to a x a y = a z , i.e., a x a y a −z = 1.…”
Section: E Exponent Equations In Baumslag-solitar Groupsmentioning
confidence: 99%
“…This has been used by several authors to obtain algorithms for groups of the form F/[N, N ], and in particular free solvable groups. Examples include the word problem (folklore, see [15]), the conjugacy problem [15,28,29,30], the power problem [15], and the knapsack problem [11,12].…”
Section: Introductionmentioning
confidence: 99%
“…In [6], Gul, Sohrabi, and Ushakov generalized Matthews result by considering the relation between the conjugacy problem in F/N and the power problem in F/N ′ , where F is a free group with a normal subgroup N and N ′ is its derived subgroup. They show that CP(F/N ′ ) is polynomial-time-Turing-reducible to CSGMP(F/N ) and CSGMP(F/N ) is Turing-reducible to CP(F/N ′ ) (no complexity bound).…”
Section: Conclusion and Open Problemmentioning
confidence: 99%
“…In [21] this has been further improved to LOGSPACE. Recently, in [6], Matthews result has been generalized to a wider class of groups without giving precise complexity bounds -see the discussion in last section.…”
Section: Introductionmentioning
confidence: 99%
“…Another possible generalization of our work is a study of groups of type F/N ′ where F is a free group and N F . Recall that the power problem in a group G is to determine if u ∈ v for given u, v ∈ G. It is shown in [7] that the conjugacy problem in F/N ′ is decidable if and only if the power problem in F/N is decidable. It would be interesting to generalize that result at least to spherical quadratic equations.…”
Section: Open Problemsmentioning
confidence: 99%