The finite irreducible linear 2-groups of degree 4
The finite irreducible linear 2-groups of degree 4
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DOI：
10.1090/memo/0613
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发表时间：
1997
影响因子：
1.9
通讯作者：
D. Flannery
中科院分区：
文献类型：
--
作者：
D. Flannery
这篇回忆录包含了GL(4，C)的有限不可约2-子群的一个完全分类。具体地说，作者提供了这类群的共轭类的代表的参数化列表，其中每个代表是通过生成一组单项矩阵来定义的。这个问题可以用各种技巧来处理，包括：初等特征标理论；刻画子模格的Hasse图的方法；以及利用Lyndon-Hochschild-Serre谱序列计算2-上同调。还讨论了所列群与其定义特征标的Schur指数同构的相关问题
This memoir contains a complete classification of the finite irreducible 2-subgroups of GL (4, C). Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by generating a set of monomial matrices. The problem is treated by a variety of techniques, including: elementary character theory; a method for describing Hasse diagrams of submodule lattices; and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups and Schur indices of their defining characters are also considered