Is it right that $\cup_{g\in G}gHg^{-1}\subsetneq G$, for every $H$, proper subgroup of infinite group $G$?
72150
Union of the conjugates of a proper subgroup
90845
Is this posible in GR $g_{ab}g^{ab}=1$?
41085
Conjugate subgroup strictly contained in the initial subgroup?
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
9612
Frattini subgroup $Φ ( G )$ is not trivial
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
128300
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
10816
Infinitely generated subgroup of a finitely one (weird)
157819
Every group of order $56$ has a proper non - trivial normal subgroup?
146760
Prove that H is a subgroup of G
156463
The complement of a proper subgroup generates the whole group
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
47539
Find an abelian infinite group such that every proper subgroup is finite
129452
Groups $G,H$ with surjective homomorphisms that are quotient of each other
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
79826
$gHg^{-1}\subset H$ whenever $Ha\not = Hb$ implies $aH\not =bH$