Equivalent condition for finite Nilpotent group
36147
A finite group is nilpotent iff two elements with relatively prime order commute
114662
Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
68955
Characterising subgroups of Prüfer $p$-groups.
64408
Subgroup of $\mathbb{Q}$ with finite index
84789
Order of products of elements in a finite Abelian group
137931
Problem from "The Theory of Finite Groups" by Kurzweil and Stellmacher
25748
If $G / Z(G)$ nilpotent then G is nilpotent.
157585
Structure theorem of finite rings
144218
Does every finite nilpotent group occur as a Frattini subgroup?
14403
If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$
13355
Product of elements of a finite abelian group
3203
Quotient group $\mathbb Z^n/\ \text{im}(A)$
59902
Example of $2$ non-isomorphic groups that have the same quotients
40846
When can a (finite) group be written as the quotient of some other group by its center?
78553
A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
125244
Equivalent definitions of normal subgroups
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent