Why if H⊴G and H is solvable and G/H is solvable, then G is also solvable?
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
111703
If $H \leq G$ and $[G:H]! \leq |G|$ then $G$ is not simple
43645
Show that $G/H\cong S_3$
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
95299
What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
98145
If $G$ is cyclic then $G/H$ is cyclic?
43750
Subgroups of finite solvable groups. Solvable?
111024
Does $gHg^{-1}\subseteq H$ imply $gHg^{-1}= H$?
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
140962
Counterexamples for $G \times H$ isomorphic to $G$ implies $H$ trivial.
58654
If $|A| > \frac{|G|}{2} $ then $AA = G $
40383
Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
90845
Is this posible in GR $g_{ab}g^{ab}=1$?
140471
Is $ G \cong G/N \times N$?
102859
Proving that $G$ is a group if $a*x=b$ and $y*a=b$ have solutions.