Hopkins and Mahowald gave a simple description of the mod $p$$p$ Eilenberg Mac Lane spectrum ${\mathbb{F}}_p$${\mathbb{F}}_p$ as the free ${\mathbb{E}}_2$${\mathbb{E}}_2$-algebra with an equivalence of $p$$p$ and 0. We show for each faithful 2-dimensional representation $\lambda$$\lambda$ of a $p$$p$-group $G$$G$ that the $G$$G$-equivariant Eilenberg Mac Lane spectrum ${\underline{\mathbb{F}}}_p$${\underline{\mathbb{F}}}_p$ is the free ${\mathbb{E}}_{\lambda }$${\mathbb{E}}_{\lambda }$-algebra with an equivalence of $p$$p$ and 0. This unifies and simplifies recent work of Behrens, Hahn, and Wilson, and extends it to include the dihedral 2-subgroups of $O(2)$$O(2)$. The main new idea is that ${\underline{\mathbb{F}}}_p$${\underline{\mathbb{F}}}_p$ has a simple description as a $p$$p$-cyclonic module over $\mathrm{THH}({\mathbb{F}}_p)$$\mathrm{THH}({\mathbb{F}}_p)$. We show that our result is the best possible one in that it gives all groups $G$$G$ and representations $V$$V$ such that ${\underline{\mathbb{F}}}_p$${\underline{\mathbb{F}}}_p$ is the free ${\mathbb{E}}_V$${\mathbb{E}}_V$-algebra with an equivalence of $p$$p$ and 0.

中文翻译：

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Eilenberg Mac Lane 光谱作为 p-旋风 Thom 光谱

Hopkins 和 Mahowald 对 mod 进行了简单的描述$p$$p$艾伦伯格麦克莱恩谱${\mathbb{F}}_p$${\mathbb{F}}_p$作为免费的${\mathbb{乙}}_2$${\mathbb{E}}_2$- 等价的代数$p$$p$和 0. 我们展示了每个忠实的二维表示$\lambda$$\lambda$一个$p$$p$-团体$G$$G$那个$G$$G$- 等变 Eilenberg Mac Lane 谱${\underline{\mathbb{F}}}_p$${\underline{\mathbb{F}}}_p$是免费的${\mathbb{乙}}_{\lambda }$${\mathbb{E}}_{\lambda }$- 等价的代数$p$$p$和 0. 这统一和简化了 Behrens、Hahn 和 Wilson 最近的工作，并将其扩展到包括二面体 2-子群$○(2)$$O(2)$. 主要的新想法是${\underline{\mathbb{F}}}_p$${\underline{\mathbb{F}}}_p$有一个简单的描述$p$$p$-旋风模块结束$\mathrm{THH}({\mathbb{F}}_p)$$\mathrm{THH}({\mathbb{F}}_p)$. 我们表明我们的结果是最好的结果，因为它为所有组提供了$G$$G$和陈述$五$$V$这样${\underline{\mathbb{F}}}_p$${\underline{\mathbb{F}}}_p$是免费的${\mathbb{乙}}_{五}$${\mathbb{E}}_V$- 等价的代数$p$$p$和 0。