Is there any abelian group whose Schur multiplier is $\mathbb{Z}_p\times \mathbb{Z}_p$?
123699
Schur multiplier as a subgroup in finite abelian groups.
122698
Construction of multiplicative group of complex numbers
30825
Infinite coproduct of abelian groups
59211
Product of Finite Abelian Group
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
3907
Abelian quotient group
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
141125
Group with order $p^2$ must be abelian . How to prove that?
13355
Product of elements of a finite abelian group
119648
For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
123219
What is multiplicative group $\bar{\mathbb{F}}_p^*$ for algebraic closure $\bar{\mathbb{F}}_p$ of $\mathbb{F}_p$ where $p$ is prime?
108425
Problem on abelian group
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
106123
Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
75068
subgroups of $\mathbb Z / 2 \mathbb Z \times \mathbb Z / 2 \mathbb Z$
31380
Exponent and abelian groups
143550
Order of product of two elements in an abelian group