Isomorphic free groups $F(A),F(B)$ induce bijective sets $A \cong B$
58766
free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$
140865
Rings' second isomorphism theorem
158892
Surjective endomorphism of abelian group is isomorphism
57309
Show that the free group on $n$ generators is a finite index subgroup of $F_2$
61084
Examples of non-isomorphic fields with isomorphic group of units and additive group structure
148569
Embeddings $A → B → A$, but $A \not\cong B$?
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
83109
Formation of the free group on $S$ is a functor
25728
A second isomorphism theorem for action on cosets
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
108044
Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
56234
Isomorphism $f$ preserves the order of an element?
95086
Homeomorphism is bijective
35353
Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?
99538
Non-trivial groups pairwise non-isomorphic with isomorphic direct products
67451
Building a bijection from a finite union of countable sets to $\mathbb{N}$