Why are the group axioms what they are?
107216
What's so special about the group axioms?
30329
Why is the collection of all groups a proper class rather than a set?
48030
Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem.
33819
What does "the ${\bf N}$ of a group" mean?
56650
Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
7865
Complete Newbie: Axiom of Foundation Exercise
2458
Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why?
45623
Axiom of Choice: What exactly is a choice, and when and why is it needed?
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
93147
Topological groups, why need them?
9158
Proving that a propositional theory of any cardinality has an independent set of axioms
84562
Proof using only field axioms
40846
When can a (finite) group be written as the quotient of some other group by its center?
950
Doubts on the axiom of union?
92050
Poincaré's theorem about groups
21374
What is exactly the difference between a definition and an axiom?
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)