How to prove G is a group
33233
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
102859
Proving that $G$ is a group if $a*x=b$ and $y*a=b$ have solutions.
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
5226
Prove that a finite semigroup G with identity is a group if and only if G contains only one idempotent
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
107716
Show that $G$ is cyclic
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
21217
$G$, group. $a,b\in G$. Show that $|a|=|a^{-1}|; |ab|=|ba|$, and $|a|=|cac^{-1}|, \forall c\in G$.
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
27905
Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. Prove that $G $ is an abelian group.
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
62455
Prove Equivalence Relation in G
98542
Prove that $H$ is a subgroup of an abelian group $G$
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
131031
Q: Proving G is d-colorable