关于晶体群非交换张量平方的几点思考
Some considerations on the nonabelian tensor square of crystallographic groups
摘要：
多环群$G$的非交换张量平方$G\otimes G$是一个多环群，它的结构在许多场合引起了人们的兴趣。同样的断言对于更广泛的可解群类仍然成立。这促使我们在两个层次上进行研究：一方面，通过研究$G$的Hirsch长度，来研究$G\otimes G$的Hirsch长度的增长;另一方面，研究有限余类的亲-- $p$ --群的非交换张量积，这类群是一类非常出色的无中心可解群，并对它们的Hirsch长度进行了研究.在其他结果中，舒尔乘数的限制将被讨论。
英文摘要：
The nonabelian tensor square $G\otimes G$ of a polycyclic group $G$ is a polycyclic group and its structure arouses interest in many contexts. The same assertion is still true for wider classes of solvable groups. This motivated us to work on two levels in the present paper: on a hand, we investigate the growth of the Hirsch length of $G\otimes G$ by looking at that of $G$, on another hand, we study the nonabelian tensor product of pro--$p$--groups of finite coclass, which are a remarkable class of solvable groups without center, and then we do considerations on their Hirsch length. Among other results, restrictions on the Schur multiplier will be discussed.
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