When is a group isomorphic to a non-trivial quotient group of itself?
27436
Does $G\cong G/H$ imply that $H$ is trivial?
61084
Examples of non-isomorphic fields with isomorphic group of units and additive group structure
45770
Does the order, lattice of subgroups, and lattice of factor groups, uniquely determine a group up to isomorphism?
113413
How do I show that two groups are not isomorphic?
23279
Group Theory Isomorphism
933
How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
27670
Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
70658
Isomorphism between quotient modules
18160
How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
40069
The image of a homomorphism is a group?
37351
Group of Order $p^2$ Isomorphic to $\mathbb{Z}_{p^2}$ or $\mathbb{Z}_{p}$ $\times$ $\mathbb{Z}_{p}$
8066
Sort-of-simple non-Hopfian groups
99538
Non-trivial groups pairwise non-isomorphic with isomorphic direct products
84869
Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
90616
When is mapping $g$ to $g^{-1}$ a group homomorphism?