How to prove: if $\forall a,b,c$, $ab=ac\Rightarrow b=c$ and $ba=ca\Rightarrow b=c$ then $(G,\circ)$ is a group
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
92430
Show that the group is cyclic.
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
29717
Not sure how to go about this group theory proof
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
3462
Proving a set of automorphisms of a group is a group under composition
158074
Cyclic group $G$ with generator $ab$.
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
17510
Proving a set is an abelian group.
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
150738
Proof of $(A - B) - C = A - (B \cup C)$
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$