query: Prove that a group where $a^2=e$ for all $a$ is commutative
positive_passages.docid: 20679
positive_passages.text: Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
negative_passages.docid: 70394
negative_passages.text: Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
negative_passages.docid: 30794
negative_passages.text: Commutator Group of $GL_2(R)$ is $SL_2(R)$
negative_passages.docid: 123610
negative_passages.text: How to show that the commutator subgroup is a normal subgroup
negative_passages.docid: 145397
negative_passages.text: How to prove that for every $i$, $a_i = i$
negative_passages.docid: 49527
negative_passages.text: Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
negative_passages.docid: 13631
negative_passages.text: Showing group with $p^2$ elements is Abelian
negative_passages.docid: 109109
negative_passages.text: Show that $E(XE[X|G])=E[(E[X|G)^2]$
negative_passages.docid: 131671
negative_passages.text: Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
negative_passages.docid: 99346
negative_passages.text: Prove a result on transitive group actions.
negative_passages.docid: 58707
negative_passages.text: Prove Quotient Group Isomorphism
negative_passages.docid: 92962
negative_passages.text: Rings with $a^5=a$ are commutative
negative_passages.docid: 158490
negative_passages.text: Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
negative_passages.docid: 144988
negative_passages.text: Commutator Subgroup of Direct Product equals the Direct Product of the Commutator Subgroups
negative_passages.docid: 45760
negative_passages.text: if G is generated by {a,b} and ab=ba, then prove G is Abelian
negative_passages.docid: 94239
negative_passages.text: Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
negative_passages.docid: 29717
negative_passages.text: Not sure how to go about this group theory proof