If in a semigroup $S$, $\forall x \exists ! y:xyx=x$, then $S$ is a group
14097
A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$
152191
Why is a monoid with right identity and left inverse not necessarily a group?
18330
Does $R[x] \cong S[x]$ imply $R \cong S$?
112407
Set of left cosets is a group
17510
Proving a set is an abelian group.
103002
Group equals union of two subgroups
133762
A set which satisfies all conditions for a Group except associativity
7536
Is there an idempotent element in a finite semigroup?
26624
Prove that is group is abelian
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
117414
How would I prove what elements $S_3$ contains, and what its subgroups are?
117701
Let $G$ be a group and $X$ set. $a,b \in X$ are in the same orbit, so show that $stab(a) \cong stab (b)$
33196
show that A(T) is a group under operation of composition of functions
19683
Is a semigroup $G$ with left identity and right inverses a group?
6755
A finite, cancellative semigroup is a group
57421
If $\forall x \in G$ where G is a group $x=x^{-1}$ then how is this group abelian?
58766
free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$