论文标题
在某些野外自动形态固定的不可减至的字符的程度上
On the degrees of irreducible characters fixed by some field automorphism, p-solvable groups
论文作者
论文摘要
众所周知，如果有限群体的所有实现的不可减值字符具有奇怪的程度，那么该组的Sylow $ 2 $ -SubGroup。我们将此结果概括为Sylow $ p $ -subgroups，对于任何质数$ p $，同时假设该组为$ p $ -solvable。特别是，如果$ p $不划分订单$ p $的现场自动形态，则证明一个$ p $ -solvibable组具有正常的Sylow $ p $ -subgroup。
It is known that, if all the real-valued irreducible characters of a finite group have odd degree, then the group has normal Sylow $2$-subgroup. We generalize this result for Sylow $p$-subgroups, for any prime number $p$, while assuming the group to be $p$-solvable. In particular, it is proved that a $p$-solvable group has a normal Sylow $p$-subgroup if $p$ does not divide the degree of any irreducible character of the group fixed by a field automorphism of order $p$.
