Proving $G$ to be a group
14097
A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$
60208
Proof of property of abelian group
102622
K is a subgroup of G. Show that K is not a normal subgroup
46863
Show that $g$ is injective
58707
Prove Quotient Group Isomorphism
114522
Prove that identity is unique in a group
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian
56650
Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
95229
Qualifying Exam Question On Elementary Group Theory
29717
Not sure how to go about this group theory proof
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.