Geodesic
Center of some solvable groups with one defining relation
Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 925-931 
E. I. Timoshenko. Center of some solvable groups with one defining relation. Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 925-931. http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a12/
@article{MZM_1998_64_6_a12,
     author = {E. I. Timoshenko},
     title = {Center of some solvable groups with one defining relation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {925--931},
     year = {1998},
     volume = {64},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions for the center of a metabelian group with one defining relation to be nontrivial are found. The center of such a group is described. The center of a group of the form $F/N'\langle g\rangle^F$ is studied under certain conditions. By means of a new technique, the recent result of A. F. Krasnikov and the author on the center of a group of the above form is sharpened.

[1] Kourovskaya tetrad. Nereshennye voprosy teorii grupp, 13-e izd., Novosibirsk, 1995

[2] Timoshenko E. I., “Tsentr gruppy s odnim opredelyayuschim sootnosheniem v mnogoobrazii metabelevykh grupp”, Sib. matem. zh., 14:6 (1973), 1351–1355 | MR | Zbl

[3] Kargapolov M. I., Izbrannye trudy. Gruppy, Nauka, Novosibirsk, 1991 | Zbl

[4] Krasnikov A. F., Timoshenko E. I., Dva zamechaniya o gruppakh vida $F/[N,N]$, Dep. VINITI No 4567–V85, VINITI, M., 1985

[5] Bachmuth S., “Automorphisms of free metabelian groups”, Trans. Amer. Math. Soc., 118 (1965), 93–104 | DOI | MR | Zbl

[6] Maltsev A. I., “Ob uravnenii $zxyx^{-1}y^{-1}z^{-1}=aba^{-1}b^{-1}$ v svobodnoi gruppe”, Algebra i logika, 1:5 (1962), 45–50 | MR | Zbl

[7] Bachmuth S., Formanek E., Mochizuki H. Y., “$IA$-automorphisms of two-generator torsion-free groups”, J. Algebra, 40:1 (1976), 19–30 | DOI | MR | Zbl

[8] Timoshenko E. I., “O primitivnykh elementakh svobodnykh grupp mnogoobrazii $\frak{AN}_n$”, Matem. zametki, 61:6 (1997), 884–889 | MR | Zbl