论文标题
关于由模块化组代数确定的组不变剂：甚至是奇数特征
On group invariants determined by modular group algebras: even versus odd characteristic
论文作者
论文摘要
让$ p $是一个奇怪的素数，让$ g $为有限的$ p $ group，带有环状换向器子组$ g'$。我们证明，在任何特征$ p $的领域，$ g $ $ g $的$ g'$ in $ g $的指数和阿贝尔化由$ g $确定。此外，如果$ g $是$ 2 $生成的，那么几乎所有确定$ g $同构的数值不变性均由同一组代数确定；结果，确定了$ g'$的中央器的同构类型。这些声明被称为$ p = 2 $的假。
Let $p$ be a an odd prime and let $G$ be a finite $p$-group with cyclic commutator subgroup $G'$. We prove that the exponent and the abelianization of the centralizer of $G'$ in $G$ are determined by the group algebra of $G$ over any field of characteristic $p$. If, additionally, $G$ is $2$-generated then almost all the numerical invariants determining $G$ up to isomorphism are determined by the same group algebras; as a consequence the isomorphism type of the centralizer of $G'$ is determined. These claims are known to be false for $p=2$.
