Are there nonisomorphic, finitely generated groups that surject onto each other?
129452
Groups $G,H$ with surjective homomorphisms that are quotient of each other
117965
Does there exist some sort of classification of incompressible groups?
111168
Automorphisms of a finite non-abelian group
147512
Is there difference between finitely presented groups and finitely generated groups?
114662
Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
115574
Finitely presented group with fewer relations than generators.
68728
Why does the natural ring homomorphism induce a surjective group homomorphism of units?
47617
Are groups with all the same Hom sets already isomorphic?
128443
Isomorphism between finite groups
147366
What are a few examples of noncyclic finite groups?
85379
Semigroup analogue to the classification of finite simple groups?
8066
Sort-of-simple non-Hopfian groups
129830
A group with no proper non-trivial subgroups
97878
Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
130937
Embeddings of finite groups into $\mathrm{GL}_n(\mathbb{Z})$
82310
Epimorphisms from a free group onto a free group
642
Does a surjective ring homomorphism have to be surjective on the unit groups?