2 problems

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Strong co-Hopfianity conjecture for rank-one sp-groups
Rank-one sp-group conjecture. Then $G$ is always strongly co-Hopfian, regardless of whether $T$ is strongly co-Hopfian.
Conjectureopenabelian-groups co-hopfian-groups p-groupsarXiv posted 3 days ago
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The non-trivial self-cover conjecture for infra-nilmanifolds
The non-trivial self-cover conjecture. The infra-nilmanifold $\Gamma \backslash G$ admits a non-trivial self-cover if and only if the nilmanifold $N \backslash G$ admits an expandi…
Conjectureopenco-hopfian-groups infra-nilmanifolds self-coversarXiv posted 3 days ago

Strong co-Hopfianity conjecture for rank-one sp-groups