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It's said that most groups arise through their actions. For instance, Galois groups arise in Galois theory as automorphisms of field extensions. Linear groups arise as automorphisms of vector spaces, ...

One of the main reasons I only supervised one PhD student is that I find it hard to find an appropriate topic for a PhD project. A good approach, in my view, is to have on the one hand a list of ...

Please list some examples of common examples of algebraic structures. I was thinking answers of the following form. "When I read about a [insert structure here], I immediately think of [example]." ...