Let $p$ be an arbitrary prime number and $G$ be an abelian group, how is $pG$ defined?
91287
Is $G/pG$ is a $p$-group?
6030
Group of order 15 is abelian
66877
Showing groups of order $p^{k}(p+1)$ are not simple, p prime
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
139100
A question on the group algebra $k[G]$ of a finite abelian group
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
24966
Converse of Lagrange's theorem for abelian groups
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
51373
$G$ non abelian, order $p^3$ ($p$ prime). Suppose that the center is $p^2$, prove that $\exists\ x$ outside of the center, of order p
68733
If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
76446
Why are cyclic groups of order $p$ (prime) unique up to isomorphism?
39976
If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?
135188
Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
112993
Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
98647
$G$ is Topological $\implies$ $\pi_1(G,e)$ is Abelian
152481
If order of group is $p^2$, where $p$ is prime, how can you deduce $G$ is isomorphic to $C_{p^2}$ or $C_p \times C_p$?
62603
Characterizations of the $p$-Prüfer group