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This article is cited in 3 scientific papers (total in 3 papers)
Primitive elements of the free groups of the varieties $\mathfrak A\mathfrak N_n$
E. I. Timoshenko Novosibirsk Engineering Building Institute
Abstract:
For groups of the form $F/N'$, we find necessary and sufficient conditions for an element $g\in N/N'$ to belong to the normal closure of an element $h\in F/N'$. It is proved that, in contrast to the case of a free metabelian group, for a free group of the variety $\mathfrak A\mathfrak N_2$, there exists an element $h$ whose normal closure contains a primitive element $g$, but the elements $h$ and $g^{\pm1}$ are not conjugate. In the group $F(\mathfrak A\mathfrak N_2)$, two nonconjugate elements are chosen that have equal normal closures.
DOI:
https://doi.org/10.4213/mzm1572
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English version:
Mathematical Notes, 1997, 61:6, 739–743
Bibliographic databases:
UDC:
512.54 Received: 19.12.1995
Citation:
E. I. Timoshenko, “Primitive elements of the free groups of the varieties $\mathfrak A\mathfrak N_n$”, Mat. Zametki, 61:6 (1997), 884–889; Math. Notes, 61:6 (1997), 739–743
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz1572https://doi.org/10.4213/mzm1572 http://mi.mathnet.ru/eng/mz/v61/i6/p884
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This publication is cited in the following articles:
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E. I. Timoshenko, “Center of some solvable groups with one defining relation”, Math. Notes, 64:6 (1998), 798–803
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Timoshenko, EI, “Test elements and test rank of a free metabelian group”, Siberian Mathematical Journal, 41:6 (2000), 1200
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Ekici N., Esmerligil Z., Ersalan D., “Ideals and primitive elements of some relatively free Lie algebras”, SpringerPlus, 5 (2016), 833
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