Abstract We aim in this paper to investigate the connections between some properties of blocks and of their dominating blocks. We find conditions to verify that a block is inertial if and only if its dominating block is inertial. In some situations the equality of the factor fusion systems associated with a block and with its Brauer correspondent block give information about the hyperfocal subgroups.

中文翻译：

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块、融合系统和超焦亚组的支配地位

摘要 我们在本文中旨在研究块的某些属性与其主导块之间的联系。我们找到条件来验证一个块是惯性的，当且仅当其主导块是惯性的。在某些情况下，与块相关联的因子融合系统及其 Brauer 对应块的相等性提供了有关超焦子群的信息。