Some extensions in the Adams spectral sequence and the 51–stem

@article{Wang2018SomeEI,
  title={Some extensions in the Adams spectral sequence
and the 51–stem},
  author={Guozhen Wang and Zhouli Xu},
  journal={Algebraic \& Geometric Topology},
  year={2018}
}
We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2-primary part of $\pi_{51}$ is $\mathbb{Z}/8\oplus\mathbb{Z}/8\oplus\mathbb{Z}/2$. This was the last unsolved 2-extension problem left by the recent works of Isaksen and the authors (\cite{Isa1}, \cite{IX}, \cite{WX1}) through the 61-stem. The proof of this result uses the $RP^\infty$ technique, which was introduced by the authors in \cite{WX1} to prove $\pi_{61}=0$. This paper… 
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