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Questions on group theory which concern finite groups.

17 votes
5 answers
1k views

Does the map $\mathrm{SL}(n,\mathbb{Z}/p^2) \rightarrow \mathrm{SL}(n,\mathbb{Z}/p)$ split?

$\DeclareMathOperator\SL{SL}$ $\DeclareMathOperator\GL{GL}$The question is the one in the title: for a prime $p$, does the obvious surjection $\pi\colon \SL(n,\mathbb{Z}/p^2) \rightarrow \SL(n,\mathbb …