论文标题
$ p $组的Schur乘数指数具有良好功率结构的引理
A lemma on the exponent of Schur multiplier of $p$ groups with good power structure
论文作者
论文摘要
在本说明中，我们简短证明了众所周知的结果，即Schur乘数$ \ m $的指数将有限$ \ p $ - 最大级别的$ \ g $的指数分配给了$ \ g $的指数。此外，对于有限$ \ p $ -group $ \ g $满足$ \ g^{\ p^2} \ subsetγ_ {\ p}（\ g）$，以及$ 3 $ - 类$ 5 $的$ 3 $ groups。我们通过证明普遍的引理来做到这一点，并表明这三类组满足了我们的引理假设。
In this note, we give short proofs of the well-known results that the exponent of the Schur multiplier $\M$ divides the exponent of $\G$ for finite $\p$-groups of maximal class and potent $\p$-groups. Moreover, we prove the same for a finite $\p$-group $\G$ satisfying $\G^{\p^2}\subset γ_{\p}(\G)$, and for $3$-groups of class $5$. We do this by proving a general lemma, and show that these three classes of groups satisfy the hypothesis of our lemma.
