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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1983 Volume 122(164), Number 3(11), Pages 313–340 (Mi sm2297)

Residual finiteness with respect to conjugacy of free polynilpotent groups

Yu. A. Kolmakov


Abstract: In this paper conditions are obtained for the residual finiteness with respect to conjugacy of groups of the form $F/R_k$, where $F$ is a free group, $R\triangleleft F$, and $R_k$ is the $k$th term of the lower central series of $R$. It is shown that free polynilpotent groups are residually finite with respect to conjugacy.
The proof utilizes an embedding of groups of the form $F/R_k$ into a twisted wreath product of simpler groups. Properties of this embedding are also studied.
Bibliography: 12 titles.

UDC: 519.4

MSC: Primary 20E26, 20E05, 20F18; Secondary 20E22

Received: 21.12.1982


 English version:
Mathematics of the USSR-Sbornik, 1985, 50:2, 299–323

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