an:03914562
Zbl 0573.20029
Myasnikov, A. G.
Extended Nielsen transformations and triviality of a group
EN
Math. Notes 35, 258-261 (1984); translation from Mat. Zametki 35, 491-495 (1984).
0001-4346 1573-8876
1984
j
20F05 20F10 55Q99 20F38 55P99
Andrews-Curtis problem; trivial group; finite balanced presentation; elementary Nielsen transformation; solvable groups
It was conjectured by \textit{J. J. Andrews} and \textit{M. L. Curtis} [Proc. Am. Math. Soc. 16, 192-195 (1965; Zbl 0131.38301) and Am. Math. Mon. 73, 21-28 (1966; Zbl 0135.044)] that if the trivial group has a finite balanced presentation \(<x_ 1,...,x_ n|\) \(r_ 1,...,r_ n>\) then \(\{r_ 1,...,r_ n\}\) can be transformed into \(\{x_ 1,...,x_ n\}\) by a sequence of transformations each of which is either an elementary Nielsen transformation or else consists of replacing some element by a conjugate. The author gives a proof of this conjecture in the variety of solvable groups.
G.Rosenberger
0131.38301; 0135.044