论文标题
置换模块的有限复合物
Bounded complexes of permutation modules
论文作者
论文摘要
令$ k $为特征$ p> 0 $的字段。对于$ g $，一个小学的Abelian $ p $ - 组，存在置换模块的集合，因此，如果$ c^*$是任何确切的有限型复合体，其条款是该集合中的模块的副本总和，则$ c^*$是合约的。结果是，如果$ g $是任何有限的组，其sylow $ p $ -subgroups不是循环或四元组，并且如果$ c^*$是一个有界的精确复合物，以至于每个$ c^i $均为一个二维模块和投影模块的直接总和，那么$ c^*$是合同的。
Let $k$ be a field of characteristic $p > 0$. For $G$ an elementary abelian $p$-group, there exist collections of permutation module such that if $C^*$ is any exact bounded complex whose terms are sums of copies of modules from the collection, then $C^*$ is contractible. A consequence is that if $G$ is any finite group whose Sylow $p$-subgroups are not cyclic or quaternion, and if $C^*$ is a bounded exact complex such that each $C^i$ is direct sum of one dimensional modules and projective modules, then $C^*$ is contractible.
