Are finitely generated solvable groups polycyclic?
125668
A proof that BS(1,2) is not polycyclic
64408
Subgroup of $\mathbb{Q}$ with finite index
34552
Proper subgroups of non-cyclic p-group cannot be all cyclic?
139611
Can a normal subgroup of a finite nonabelian group be nonabelian?
145254
$G$ be a non-nilpotent and supersoluble finite group.
145159
Finite group is abelian if the representatives of its conjugacy classes commute
126590
Why is the multiplicative group of a finite field cyclic?
158074
Cyclic group $G$ with generator $ab$.
147366
What are a few examples of noncyclic finite groups?
152954
Extensions of finite cyclic groups
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
29635
Fields finitely generated as $\mathbb Z$-algebras are finite?
76446
Why are cyclic groups of order $p$ (prime) unique up to isomorphism?
29003
Is the dihedral group $D_n$ nilpotent? solvable?
109801
multiplicative group of infinite fields
151619
A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.