关于第二类有限群的能力与素指数
On the capability of finite groups of class two and prime exponent
摘要：
研究了奇素指数的二阶$p$ -群的能力.证明了能力问题等价于向量空间和线性变换的一个命题，并利用等价性给出了一些旧结果和几个新结果的证明.特别是，我们建立了一些新的必要条件和新的充分条件的能力，包括一个充分条件的基础上，只有排名的$G/Z(G)$和$[G,G]$。最后，我们在这个类中的5个生成的组中划分出有能力的组。
英文摘要：
We consider the capability of $p$-groups of class two and odd prime exponent. The question of capability is shown to be equivalent to a statement about vector spaces and linear transformations, and using the equivalence we give proofs of some old results and several new ones. In particular, we establish a number of new necessary and new sufficient conditions for capability, including a sufficient condition based only on the ranks of $G/Z(G)$ and $[G,G]$. Finally, we characterise the capable groups among the 5-generated groups in this class.
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