论文标题
对称组的Sylow子组的线性字符
Linear characters of Sylow subgroups of symmetric groups
论文作者
论文摘要
让$ p $成为任何素数。令$ p_n $为对称组$ s_n $的Sylow $ p $ -subgroup。令$ ϕ $和$ψ$为$ p_n $的线性字符，让$ n $为$ s_n $的$ p_n $的正常人。在本文中，我们表明，$ ϕ $和$ψ$对$ s_n $的电感相同，并且只有当$ ϕ $和$ψ$是$ n $ - conjugate时。这是纳瓦罗（Navarro）$ p $可销售组的对称组的类似物。
Let $p$ be any prime. Let $P_n$ be a Sylow $p$-subgroup of the symmetric group $S_n$. Let $ϕ$ and $ψ$ be linear characters of $P_n$ and let $N$ be the normaliser of $P_n$ in $S_n$. In this article we show that the inductions of $ϕ$ and $ψ$ to $S_n$ are equal if, and only if, $ϕ$ and $ψ$ are $N$--conjugate. This is an analogue for symmetric groups of a result of Navarro for $p$-solvable groups.
