Is conjugation in infinite groups well behaved?
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
133664
When the automorphism group is trivial......
123860
When are two direct products of groups isomorphic?
114431
Monoids and Subgroups
40094
Does $G\oplus G \cong H\oplus H$ imply $G\cong H$ in general?
87534
Finitely generated group which is not finitely presented
100149
If there are injective homomorphisms between two groups in both directions, are they isomorphic?
28210
A finite group with exactly $2$ conjugacy classes isomorphic to $\mathbb{Z}_2$
84397
$x$ conjugate to $y$ in a group $G$ is an equivalence relation on $G$
21243
Kaplansky's theorem of infinitely many right inverses in monoids?
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
153721
Conjugating a permutation
145159
Finite group is abelian if the representatives of its conjugacy classes commute
123677
Normal subgroups of infinite symmetric group
63162
Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
29445
Trying to prove that $H=\langle a,b:a^{3}=b^{3}=(ab)^{3}=1\rangle$ is a group of infinite order.