论文标题
$ q $ tensor产品的扩展的某些结构和关闭属性，$ q \ geq 0 $
Some Structural and Closure Properties of an Extension of the $q$-tensor Product of Groups, $q \geq 0$
论文作者
论文摘要
在这项工作中，我们研究了组$η^q（g，h）$，$ q $的某些结构性属性，这是$ q $ -tensor产品$ g \ otimes^q h）$的延伸，其中$ g $ g $和$ h $是某些Group $ l $的正常子组。我们通过简单的参数建立$η^q（g，h）$的一些封闭属性，当$ g $和$ h $属于某些Schur类时。这扩展了有关文献中发现的情况$ q = 0 $的相似结果。将我们的注意事项限制为$ g = h $，我们计算$ q $ -tensor square $ d_n \ otimes^q d_n $ for $ q $奇数，其中$ d_n $表示dihedral of订单$ 2N $。还为$ g \ otimes^q g $指数的上限建立了nilpotent $ g $ class $ \ leq 3 $的$ g $，该组扩展到所有$ q \ geq 0 $类似的限制。
In this work we study some structural properties of the group $η^q(G, H)$, $q$ a non-negative integer, which is an extension of the $q$-tensor product $G \otimes^q H)$, where $G$ and $H$ are normal subgroups of some group $L$. We establish by simple arguments some closure properties of $η^q(G,H)$ when $G$ and $H$ belong to certain Schur classes. This extends similar results concerning the case $q = 0$ found in the literature. Restricting our considerations to the case $G = H$, we compute the $q$-tensor square $D_n \otimes^q D_n$ for $q$ odd, where $D_n$ denotes the dihedral group of order $2n$. Upper bounds to the exponent of $G \otimes^q G$ are also established for nilpotent groups $G$ of class $\leq 3$, which extend to all $q \geq 0$ similar bound found by Moravec in [21].
