Thompson 群的一个新数量刻画
Journal: Modern Education Forum DOI: 10.32629/mef.v9i2.19154
Abstract
设G 是有限群,π(G)为G 的阶的素因子的集合,pm 为π(G)的最大元,πpm (G)表示群G的pm 阶元中心化子的阶的集合。本文利用群的偶阶分量与群的G 最高阶元中心化子的阶的集合给出了Thompson群Th 的一个数量刻画。我们证明：有限群G 与散在单群M 同构当且仅当：(1)G 与M 的偶阶分量m1 完全相同；(2)πpm (G)=πpm (M ),这里M 是有限单群Th。
Keywords
有限单群；散在单群；偶阶分量；中心化子
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