Does there always exists an injective homomorphism from $G$ into $S_m$ for $m<n$
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
27728
Question on a homomorphism of a set G.
121244
Homomorphisms and automorphisms on polynomial rings
46355
If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?
97878
Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
126930
Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
133660
When can a homomorphism be determined entirely by its generators
11202
If $g \circ f$ is injective, so is $g$
100149
If there are injective homomorphisms between two groups in both directions, are they isomorphic?
151047
a non trivial example: $G/H$ is isomorphic to $G$
27670
Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
78913
In a finite field, is there ever a homomorphism from the additive group to the multiplicative group?
115999
Is there always an injective map from a space in its dual space?
129858
"Almost" ring homomorphism
51695
Finding all homomorphisms between $\mathbb{Z}/m\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$
148616
When is a ring homomorphism $A \to A$ surjective but not injective.
158396
Finite $G$ with involutory automorphism $\alpha$ with no nontrivial fixed points. Proving properties of $\alpha$.