All Questions

Let $S$ be the set of all finite permutations of $\mathbb{N}$, i.e. they fix all but a finite set, and $A\subset S$ the set of all even permutations. Theorem. The normal subgroups of $S_\infty$ are ...

Let $\mathcal{B}$ be the (unique up to isomorphism) countable atomless boolean algebra, and $\mathrm{Aut}(\mathcal{B})$ its automorphism group, with pointwise convergence topology. My question: Does $...

Let $G$ be the automorphism group of the binary rooted tree. The downward Löwenheim-Skolem theorem states that G has a countable elementary sub-structure. My question is whether such sub-structure ...