5 votes

How can we correctly understand the definition stating that the union of conjugacy classes forms a normal subgroup?

Neither of your characterisations of normal subgroup are correct. You should re-read whatever sources you are using carefully. A subgroup $H$ of $G$ is normal if and only if for all $h \in H$, for ...
1 vote

$K \unlhd A \rightarrow \Phi(A)$ is isomorphism

There is 1-1 correspondence between $\{ A\leq G_1 : K\leq A\}$ and subgroups of $\pi (G_1) = G_1 / K$. surjective: as $\pi$ is surjective, for every subgroups $C \leq G_1 / K$ exists $\pi ^ {-1} (C) \...

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