Proving that If $\overline K \trianglelefteq \overline G$ , then $\phi^{-1}(\overline K)=\{k\in G: \phi(k)\in\overline K\}\trianglelefteq G$.
54911
The preimage of a normal subgroup under a group homomorphism is normal
137982
Show that $\textbf{ZF}$ shows $\phi$ is $\Delta_1$
125188
how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
26233
$[K(\zeta_n):K]=\phi(n)$?
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
63769
Group theory proof of Euler's theorem ($a^{\phi(m)} \equiv 1\mbox{ }(\mbox{mod }m)$ if $\gcd(a,m)=1$)
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
141683
$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
65744
How can I Prove that H=G or K=G
107842
Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
82935
Prove that f∈Θ(g)if and only ifO(f) =O(g).
117681
For which Natural $n\ge2: \phi(n)=n/2$
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$