The note identifies which which couniversal spaces have suspension spectra equivalent to commutative orthogonal ring G-spectra for a compact Lie group G. These are precisely those whose cofamily is closed under passage to finite index subgroups. Equivalently these are the couniversal spaces admitting an action of an equivariant E infinity operad.

中文翻译：

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等变可交换环谱的共通空间

注释确定哪些共性空间具有与紧李群 G 的可交换正交环 G 谱等价的悬浮谱。这些正是那些共族在通过有限索引子群时是封闭的。等价地，这些是承认等变 E 无穷大操作数的动作的公共空间。