论文标题
广义二面体CI组
Generalised dihedral CI-groups
论文作者
论文摘要
在本文中，我们发现了对CI组结构的强烈新限制。我们表明，如果$ r $是一个概括的二面体组，并且如果$ r $是Ci-group，那么对于每个奇数prime $ p $，sylow $ p $ -subgroup of $ r $ $ r $都有订单$ p $，或$ 9 $。因此，任何具有商用二面体组的CI-Group都具有相同的限制，对于该组的每个奇数$ p $ sylow $ p $ -subgroup都有订单$ p $，或$ 9 $。我们还为每个BCI组都是Ci组的猜想提供了反对例子。
In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if $R$ is a generalised dihedral group and if $R$ is a CI-group, then for every odd prime $p$ the Sylow $p$-subgroup of $R$ has order $p$, or $9$. Consequently, any CI-group with quotient a generalised dihedral group has the same restriction, that for every odd prime $p$ the Sylow $p$-subgroup of the group has order $p$, or $9$. We also give a counter example to the conjecture that every BCI-group is a CI-group.
