Conjugation of a group: what is it and where does $g⋅a = gag^{-1}$ play into it?
39550
Intuition behind conjugation in group theory
45314
Conjugacy classes of D2n?
154398
Show that H is a subgroup of G
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
30676
$G'$ and the product of all the elements in an odd order group
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
37414
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
19683
Is a semigroup $G$ with left identity and right inverses a group?
151699
Group of inner automorphisms of a group $G$
8742
Examples and further results about the order of the product of two elements in a group
45028
How to show that $\langle a \rangle$ is a subgroup of a group $G$, where $a$ is in center of the group $G$
84397
$x$ conjugate to $y$ in a group $G$ is an equivalence relation on $G$
29717
Not sure how to go about this group theory proof
139100
A question on the group algebra $k[G]$ of a finite abelian group
42213
Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
101596
Determine group G as cyclic
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?