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Selected answers:

Centralizers of pairs in monoids of self-maps

When do two non-degenerate 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

Do constructible sets have Krull dimension?