if center of Group is of index n,prove that every conjugacy class has almost n elements
93198
The order of a conjugacy class is bounded by the index of the center
107010
How many elements of order $k$ are in $S_n$?
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
131516
Subgroup generated by n-th powers of elements
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
7418
The Center of $\operatorname{GL}(n,k)$
39425
Surprising but simple group theory result on conjugacy classes
61550
Existence of elements of order $p^k$ in a finite group
59041
Centre of $GL_n(\mathbb R)$
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
19352
Normal subgroup of index m contains every element of order n where m and n are relatively prime
48393
Abelian groups of order n.
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
41695
Conjugate class in the dihedral group
7528
Index of the center of a group in the group is not a prime number
95378
Known bounds for the number of groups of a given order.
145159
Finite group is abelian if the representatives of its conjugacy classes commute