This article is cited in 7 papers

The solvability problem for equations in one unknown in nilpotent groups

N. N. Repin


Abstract: The author constructs a finitely generated nilpotent group of class 3 for which there is no algorithm recognizing the solvability of equations in one unknown. Such an algorithm exists for every finitely generated nilpotent group of class 2. It is proved that for any $c\geqslant10^{20}$ there is no algorithm recognizing the solvability of equations in one unknown in free nilpotent groups of class $c$.
Bibliography: 6 titles.

UDC: 512

MSC: Primary 20F10; Secondary 20F18

Received: 18.01.1984

 English version: Mathematics of the USSR-Izvestiya, 1985, 25:3, 601–618

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