Are finitely generated submodules of a $p$-adic module direct summands?
2026-04-02 05:19:47.1775107187
Finitely generated submodule of $p$-adic module is direct summand?
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No. The $\mathbf{Z}_p$-module $\mathbf{Q}_p/\mathbf{Z}_p$ has lots of finite subgroups that cannot be summands because they cannot be divisible.