论文标题
关于自动形态的固定点对组结构的影响
On the influence of the fixed points of an automorphism to the structure of a group
论文作者
论文摘要
让$α$成为$ g $ prime订单的二型自动形态，让$ p $为$α$ -INVARIANT SYLOW $ P $ -Subgroup $ g $。假设$ p \notinπ（c_g（α））$。首先，我们证明$ g $是$ p $ -nilpotent，并且仅当$ c_ {n_g（p）}（α）$集中$ p $时。如果$ g $是$ sz（2^r）$和$ psl（2,2^r）$ - 在$ r = |α| $的情况下免费，我们表明$ g $是$ p $ c $ cluck cluck y时且仅当$ c_g（α）$差异$ p $。这两个结果的结果是，我们获得了$ g \ cong p \ times h $ for $ h $时，并且仅当$ c_g（α）$集中$ p $时。我们还证明了Frobenius $ p $ -nilpotency定理的概括，用于承认企业命令的一组自动形态。
Let $α$ be a coprime automorphism of a group $G$ of prime order and let $P$ be an $α$-invariant Sylow $p$-subgroup of $G$. Assume that $p\notin π(C_G(α))$. Firstly, we prove that $G$ is $p$-nilpotent if and only if $C_{N_G(P)}(α)$ centralizes $P$. In the case that $G$ is $Sz(2^r)$ and $PSL(2,2^r)$-free where $r=|α|$, we show that $G$ is $p$-closed if and only if $C_G(α)$ normalizes $P$. As a consequences of these two results, we obtain that $G\cong P\times H$ for a group $H$ if and only if $C_G(α)$ centralizes $P$. We also prove a generalization of the Frobenius $p$-nilpotency theorem for groups admitting a group of automorphisms of coprime order.
