$G$ of finite order $2p$ ($p$ is prime). Prove that $G$ abelian.
126893
A group of order 2p (p prime) and other conditions - prove abelian.
67973
Prove that a finite abelian group is simple if and only if its order is prime.
59211
Product of Finite Abelian Group
14528
Proof that all abelian simple groups are cyclic groups of prime order
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
51352
Subgroups of a finite abelian group
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
41731
Question about the order of the product of two elements in an abelian group
26624
Prove that is group is abelian
4402
Group of order $pqr$, $p < q < r$ primes
71420
Prove that a group is abelian.
85579
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
68971
Elementary approach to proving that a group of order 9 is Abelian
79995
G is group of order pq, pq are primes