## Z-group wreath products.(English)Zbl 0525.20019

### MSC:

 20E22 Extensions, wreath products, and other compositions of groups 20F14 Derived series, central series, and generalizations for groups 20F19 Generalizations of solvable and nilpotent groups

### Keywords:

wreath product; Z-group; central series; locally nilpotent group
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### References:

 [1] G. Baumslag: Lecture Notes on Nilpotent Groups. Amer. Math. Soc., (Regional Conference Series in Mathematics, No. 2), Providence, RI, 1971. · Zbl 0241.20001 [2] K. W. Gruenberg: Residual properties of infinite soluble groups. Proc. London Math. Soc., (3) 7 (1957), 29-62. · Zbl 0077.02901 [3] B. Hartley: The residual nilpotence of wreath products. Proc. London Math. Soc., (3) 20 (1970), 365-392. · Zbl 0194.03402 [4] K. K. Hickin, R. E. Phillips: On classes of groups defined by systems of subgroups. Arch. Math., 24 (1973), 346-350. · Zbl 0275.20070 [5] R. D. Konyndyk: Residually central wreath products. Pac J. Math., 68 (1977), 99-103. · Zbl 0367.20031 [6] R. E. Phillips, J. E. Roseblade: A residually central group that is not a $$Z$$-group. Mich. Math. J., 25 (1978), 233-234. · Zbl 0389.20023 [7] D. J. S. Robinson: Finiteness Conditions and Generalized Soluble Groups. Part II, Springer-Verlag, Berlin) · Zbl 0243.20033
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