Proving $G\cong \Bbb{Z}_p$ if $|G|$ is prime.
13734
Show that every group of prime order is cyclic
135586
Prove that the preimage of a prime ideal is also prime.
56779
The norm of a Gaussian prime is a prime or a square of a prime in $\mathbb{Z}$
63659
If D is an Integral Domain and has finite characteristic p, prove p is prime.
61064
Finite index subgroup $G$ of $\mathbb{Z}_p$ is open.
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
156909
$\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
66313
$\mathbb{Z}[i]/(a+bi) \cong \mathbb{Z}_{a^2+b^2}$ if $(a,b)=1$
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
44496
Norm $N$ on $\Bbb Z[\sqrt d]$ is multiplicative, $N(x)$ prime $\Rightarrow x$ irreducible
118452
how to prove $\mathbb Z_n$ has divisors of zero if and only if $n$ is not prime
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
103423
Normal subgroup where G has order prime
128711
$(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?