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Selected answers:
Centralizers of pairs in monoids of selfmaps
When do two nondegenerate quadratic forms give rise to isomorphic Lie algebras?
A question about subsets of plane (or: how to apply the notion of commensurating action to a plane geometry question);
Finitely generated soluble groups with uncountably many maximal subgroups
Example of reflective subcategory of (Groups) whose reflector doesn't preserve finite products
divisors of $p^4+1$ of the form $kp+1$
Infinitely many finitely generated groups having the same Cayley graph
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