If $G_1,\cdots,G_n,\cdots$ are metrizable topological groups, then $G= \prod_{n\in \mathbb N} G_n$ is also a topological group.
58484
Is the topological product $\Pi \{G_\alpha: \alpha < \kappa\} $ a topological group?
84198
Step in Proof of Cardinality of Product of two Groups
16512
Product of $T_1$ spaces is $T_1$
62342
$x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
37379
Let $G$ a group with normal subgroups $M,N$ such that $M\cap N=\{e\}$. Show that if $G$ is generated by $M\cup N$ then $G\cong M \times N$.
11015
Given a group $ G $, how many topological/Lie group structures does $ G $ have?
11003
Proving that $G/N$ is an abelian group
63162
Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.
61394
The product of finitely many cyclic groups is cyclic
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
113013
Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
24561
$\mathbb S_n$ as semidirect product
106298
Prove that some topology is not metrizable
146952
When can I say that $\cup H_i$ is a group?
35124
Can every non-simple group $G$ be written as a semidirect product?