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Questions about the branch of algebra that deals with groups.

**9**

votes

Hall's universal group is a countable locally finite group that contains every countable locally finite group (see these lecture notes).

answered Jun 22 '10 by Someone

**1**

vote

[Slightly too long for a comment, so I post it community wiki answer.]
The kernel of the epimorphism $\quad\varphi : G\times G \to H\times H\quad$ is a normal subgroup of $G\times G$, for which by an …

answered Nov 5 '12 by Someone

**9**

votes

Let $N$ be normal in $G\times H$. For $n=(n_1, n_2) \in N$ and $(g, 1) \in G\times H$ follows $([n_1, g], 1) = (n_1^{-1}n_1^g, 1) = n^{-1}\cdot n^{(g, 1)} \in N$ (taking the notations used in group th …

answered May 6 '10 by Someone