Prove that a finite abelian group is simple if and only if its order is prime.
14528
Proof that all abelian simple groups are cyclic groups of prime order
79995
G is group of order pq, pq are primes
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
41731
Question about the order of the product of two elements in an abelian group
145563
In an abelian group, the elements of finite order form a subgroup.
133770
Subgroups of finite abelian groups.
104112
Number of finite simple groups of given order is at most $2$ - is a classification-free proof possible?
26624
Prove that is group is abelian
59211
Product of Finite Abelian Group
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
134455
Any group of order $15$ is abelian(without sylow theorem)
36147
A finite group is nilpotent iff two elements with relatively prime order commute
137715
If $[L:K]$ is prime, show that $L/K$ is a simple extension.
149750
Help understanding Fundamental Theorem of Finite Abelian Groups
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
68971
Elementary approach to proving that a group of order 9 is Abelian
143550
Order of product of two elements in an abelian group