Given finite $X \neq \emptyset$ together with an associative binary operation, if left-cancellation and right-cancellation laws hold, is $X$ a group?
6755
A finite, cancellative semigroup is a group
62286
Suppose $G$ is a semigroup and it holds both left and right cancellation.
139992
Is power-associativity finitely axiomatizable?
64582
Group covered by finitely many cosets
130418
Is ${\{\emptyset,\{\emptyset\},\{\{\emptyset\}\},\{\{\{\emptyset\}\}\},...\}} $ a set?
59187
Proof, is $\forall x : (P(x) \lor Q(x)) \Leftrightarrow \forall x : P(x) \lor \forall x : Q(x)$?
120911
Clarification on proof: Order of left cosets equal
13282
In the category $\mathbf{Set}$ is "the product of an empty set of sets a one-element set"?
154959
Proof of associativity of GCD?
70298
Are quotients of chain groups $C_n(X)/C_n(A)$ still free?
62208
If $A$ is a non-empty set, then $A \notin A$
81509
The cardinality of a countable union of countable sets, without the axiom of choice
105233
Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$?
18817
Does commutativity imply Associativity?
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
58766
free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$
84985
Is a semigroup with unique right identity and left inverse a group?