AI 中文总结
研究阶为\(p^n\)（\(p,n>2\)）的极大类\(p\)-群的指数及舒尔乘子，通过分析\(n\)与\(p\)的关系确定群指数，得出舒尔乘子指数至多为特定值，明确了极大类\(p\)-群相关指数的规律。
AI 中文摘要
设\(P\)是阶为\(p^n\)的极大类\(p\)-群，其中\(p,n>2\)。当\(n>p + 1\)时，\(P\)的指数为\(p^k\)，\(k\)是大于等于\((n - 1)/(p - 1)\)的最小整数；\(n = p + 1\)时，\(P\)的指数为\(p^2\)；\(n\leq p\)时，\(P\)的指数为\(p\)或\(p^2\)。\(P\)的舒尔乘子的指数至多为\(p^k\)，\(k\)是大于等于\((n - 2)/(p - 1)\)的最小整数。
英文摘要
Let $P$ be a $p$-group of maximal class of order $p^n$ where $p,n>2$. If $n>p+1$ then the exponent of $P$ is $p^k$, where $k$ is the least integer greater or equal to $(n-1)/(p-1)$. If $n=p+1$ then $P$ has exponent $p^2$. And if $n\leq p$ then $P$ has exponent $p$ or $p^2$, with both possibilities arising. The Schur multiplier of $P$ has exponent at most $p^k$, where $k$ is the least integer greater than or equal to $(n-2)/(p-1)$.
