Unramified Brauer groups of finite and infinite groups
Unramified Brauer groups of finite and infinite groups
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DOI：
10.1353/ajm.2012.0046
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发表时间：
2012-03
影响因子：
1.7
通讯作者：
P. Moravec
中科院分区：
文献类型：
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作者：
P. Moravec
Bogomolov乘子是同构于给定商空间的非分歧Brauer群的群理论不变量。我们推导出Bogomolov乘子的同调形式，证明了一个Hopf型公式，找到了对应于这个不变量的五项正合序列，并描述了Bogomolov乘子在中心扩张理论中的作用.本文给出了一类二阶幂零群的Bogomolov乘子的一个新的刻画。我们定义的Bogomolov乘数在K-理论和证明其平凡性是等价于解决一个长期存在的问题所造成的低音。提出了一种计算Bogomolov乘子的算法。
The Bogomolov multiplier is a group theoretical invariant isomorphic to the unramified Brauer group of a given quotient space. We derive a homological version of the Bogomolov multi- plier, prove a Hopf-type formula, find a five term exact sequence corresponding to this invariant, and describe the role of the Bogomolov multiplier in the theory of central extensions. A new description of the Bogomolov multiplier of a nilpotent group of class two is obtained. We define the Bogomolov multiplier within K-theory and show that proving its triviality is equivalent to solving a long-standing problem posed by Bass. An algorithm for computing the Bogomolov multiplier is developed.