论文标题
非亚伯张量广场的指数和$ p $ groups的相关结构
The exponent of the non-abelian tensor square and related constructions of $p$-groups
论文作者
论文摘要
令$ g $为有限的$ p $ group。在本文中，我们获得了非亚洲张量广场$ g \ otimes g $和$ν（g）$的指数的界限，这是$ g \ otimes g $ by $ g \ times g $的一定扩展。特别是，当$ \ exp（ν（g/n））$和$ \ exp（n）$时，我们限制了$ \ exp（ν（g））$，当时$ g $允许一些特定的普通子组$ n $。我们还根据$ \ exp（g）$以及nilpotency类或组$ g $的coclass建立$ \ exp（g \ otimes g）$的界限，从而改善了一些现有界限。
Let $G$ be a finite $p$-group. In this paper we obtain bounds for the exponent of the non-abelian tensor square $G \otimes G$ and of $ν(G)$, which is a certain extension of $G \otimes G$ by $G \times G$. In particular, we bound $\exp(ν(G))$ in terms of $\exp(ν(G/N))$ and $\exp(N)$ when $G$ admits some specific normal subgroup $N$. We also establish bounds for $\exp(G \otimes G)$ in terms of $\exp(G)$ and either the nilpotency class or the coclass of the group $G$, improving some existing bounds.
