A semigroup in which both the equations ax=b and ya=b have unique solution, is a group. Prove it.
102859
Proving that $G$ is a group if $a*x=b$ and $y*a=b$ have solutions.
114522
Prove that identity is unique in a group
90584
Show set of affine transformations is a group
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
87441
Proof involving matrix equation
65744
How can I Prove that H=G or K=G
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
71203
Proving that two systems of linear equations are equivalent if they have the same solutions
114906
For $n \in \mathbb{N}$ and $W \leq \mathbb{F}^n$, there exists a homogeneous system of linear equations whose solution space is $W$
37414
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
76110
Proving that the zero vector is unique
7121
If $G$ is a finite group and $|G| < |A| + |B|$, then $G=AB$.
124505
Proof that there must exist infinitely many solutions to a homogeneous system of equations when more unknowns than equations
89234
Any Set with Associativity, Left Identity, Left Inverse is a Group
99346
Prove a result on transitive group actions.
19683
Is a semigroup $G$ with left identity and right inverses a group?