A set with a binary operation and an interesting property defines a group
14097
A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$
89506
Union of disjoint sets : Equivalence relations
127123
Cardinality of power set and binary sequence
140668
Union of $2$ set $A, B$ where $ A$ is a subset of $B$
3462
Proving a set of automorphisms of a group is a group under composition
66464
Faithful group actions for singleton group or for empty set
26572
Does the Symmetric difference operator define a group on the powerset of a set?
47697
Russell's paradox: a set cannot contain its own powerset
43024
Well-ordered sets, properties of an element that is not largest in the set
56370
Associative operation on a set $S$
64658
How many associative binary operations for a set of two elements?
144362
The construction of a Vitali set
103717
Topological Property of the Set of Integers
37951
proof detail concerning bijection between a set and its power set
30329
Why is the collection of all groups a proper class rather than a set?
130771
Sets and the principle of inclusion and exclusion
104980
Possibilities for a group $G$ that acts faithfully on a set of objects with two orbits?