关于$p$ -群的圈积生成的$K_p$ -系列和簇
On $K_p$-series and varieties generated by wreath products of $p$-groups
摘要：
设$A$是有限指数的幂零$p$ -群，$B$是有限指数的交换$p$ -群.然后圈积$A {\rm Wr} B$生成簇${\rm var}(A) {\rm var}(B)$当且仅当群$B$包含同构于$p^v = \exp{(B)}$阶循环群$C_{p^v}$的至少可数个拷贝的直积$C_{p^v}^\infty$的子群。所得到的定理继续我们以前的研究情况下，${\rm var}(A {\rm Wr} B ) = {\rm var}(A){\rm var}(B)$持有的一些其他类的群体$A$和$B$（阿贝尔群，有限群等）。
英文摘要：
Let $A$ be a nilpotent $p$-group of finite exponent, and $B$ be an abelian $p$-groups of finite exponent. Then the wreath product $A {\rm Wr} B$ generates the variety ${\rm var}(A) {\rm var}(B)$ if and only if the group $B$ contains a subgroup isomorphic to the direct product $C_{p^v}^\infty$ of at least countably many copies of the cyclic group $C_{p^v}$ of order $p^v = \exp{(B)}$. The obtained theorem continues our previous study of cases when ${\rm var}(A {\rm Wr} B ) = {\rm var}(A){\rm var}(B)$ holds for some other classes of groups $A$ and $B$ (abelian groups, finite groups, etc.).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
