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If $B$ is a subalgebra of $A$, you can ask whether the $B$-module structure on $B$ can be extended to give an $A$-module structure on $B$.

W H Lin, in his 1973 PhD thesis at Northwestern, showed that the only Hopf subalgebras of the mod 2 Steenrod algebra for which this can be done are the algebras $A(n)$ — this is the algebra generated by $\text{Sq}^{2^i}$ for $i\leq n$. Are there any electronic copies of the thesis, or at least this particular proof, available?

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    $\begingroup$ this is the library entry --- no digital copy I'm afraid. $\endgroup$ – Carlo Beenakker Jan 10 '20 at 21:21
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Using @CarloBeenakker's answer, our librarian found an electronic version, produced from the microfilm copy of the original: https://search.proquest.com/docview/302701183 (full text may require accessing through a university library or similar). At a quick glimpse, it looks complete.

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