Is there a way to determine whether a representation of a finite group is faithful?
50993
Faithful representations and character tables
41363
when is f@g not the same as f[g]?
35353
Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?
78913
In a finite field, is there ever a homomorphism from the additive group to the multiplicative group?
133497
Group Membership Test for Permutations
642
Does a surjective ring homomorphism have to be surjective on the unit groups?
129476
The trace map in a finite field.
85379
Semigroup analogue to the classification of finite simple groups?
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
139912
Complexity of finite group isomorphism problem
45770
Does the order, lattice of subgroups, and lattice of factor groups, uniquely determine a group up to isomorphism?
128443
Isomorphism between finite groups
40383
Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?
145159
Finite group is abelian if the representatives of its conjugacy classes commute
40069
The image of a homomorphism is a group?
152604
For a finite group of order $2n$ does there exist $x$ such that $x\ast x=e$?
90616
When is mapping $g$ to $g^{-1}$ a group homomorphism?