Show $S_n=\mathbb{Z}_2 \rtimes A_n$
24561
$\mathbb S_n$ as semidirect product
98284
show $\Bbb Z_6 \cong \Bbb Z_3 \times \Bbb Z_2 $.
143831
Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
135018
Proving that a sequence has $a_n = a_{n+2}$ for $n$ sufficiently large.
75317
Show that $(s_n)$ is a Cauchy sequence
111348
Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
147827
How to calculate $|\operatorname {SL}_2(\mathbb Z/N\mathbb Z)|$?
129732
What is $\operatorname{Aut}(\mathbb{Z}_2\oplus \mathbb{Z}_2)$?
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
102112
Idempotents in $\mathbb Z_n$
130081
Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
134726
Show the polynomial is irreducible in $\textbf Z_2$
154076
How to show this property of $\mathbb{RP}^{n}$.
132725
Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
14403
If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$