Let $G$ be a group of order $p^2$ then $G$ is isomorphic to $\mathbb{Z}_{p^2}$ or $ \mathbb{Z}_p \times \mathbb{Z}_p$.
37351
Group of Order $p^2$ Isomorphic to $\mathbb{Z}_{p^2}$ or $\mathbb{Z}_{p}$ $\times$ $\mathbb{Z}_{p}$
23279
Group Theory Isomorphism
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
7973
Groups of order $pq$ have a proper normal subgroup
148904
Groups of order $p^3$
152481
If order of group is $p^2$, where $p$ is prime, how can you deduce $G$ is isomorphic to $C_{p^2}$ or $C_p \times C_p$?
15387
Order of $GL(n, \mathbb Z_p)$
36137
Prove $GL_2(\mathbb{Z}/2\mathbb{Z})$ is isomorphic to $S_3$
75473
If a group $G$ has odd order, then the square function is injective.
134820
$p$ prime, Group of order $p^n$ is cyclic iff it is an abelian group having a unique subgroup of order $p$
123796
Order of automorphism group of a $p$-group is divisible by $p$.
114394
Determine whether $\mathbb{Z}\times \mathbb{Z}$ and $\mathbb{Z}\times \mathbb{Z}\times \mathbb{Z}$ are isomorphic groups or not.
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
28576
Galois Groups are isomorphic to subgroups of symmetric groups.
107511
If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?