Embeddings of 𝐷𝐼₂ in 𝐹₄

Broto, Carles; Møller, Jesper

doi:10.1090/S0002-9947-01-02781-7

Embeddings of $\mathrm {DI}_2$ in $\mathrm {F}_4$
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by Carles Broto and Jesper M. Møller

Trans. Amer. Math. Soc. 353 (2001), 4461-4479

DOI: https://doi.org/10.1090/S0002-9947-01-02781-7

Published electronically: May 3, 2001

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Abstract:

We show that there is only one embedding of $\mathrm B\mathrm {DI}_2$ in $\mathrm B\mathrm {F}_4$ at the prime $p=3$, up to self-maps of $\mathrm B\mathrm {DI}_2$. We also describe the effect of the group of self-equivalences of $\mathrm B\mathrm {F}_4$ at the prime $p=3$ on this embedding and then show that the Friedlander exceptional isogeny composed with a suitable Adams map is an involution of $\mathrm B\mathrm {F}_4$ whose homotopy fixed point set coincide with $\mathrm B\mathrm {DI}_2$

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