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Q: Prove that the set of all algebraic numbers is countable: proof using fundamental theorem of algebra
I'm doing exercises in Rudin's real analysis, chapter 2. More particularly, I'm making exercise 2 of that chapter. I already noticed there were other threads about this exercise on the site, but in order to not spoil myself, I rather avoid them until I know my solution is correct.
So here's the ...
The following problem is from the book "Finite Group Theory" by Martin Isaacs.
(2.A.7) Let $S \lhd \lhd G$ (S is subnormal in G), where $S$ is nonabelian and simple and $G$ is finite. Show that $S^{G}$, the normal closure of $G$ is minimal normal subgroup in $G$
HINT: Work by induction ...
