query: Group commutator relations and the neutral element.
positive_passages.docid: 23517
positive_passages.text: Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
negative_passages.docid: 125613
negative_passages.text: Free idempotent semigroup with 3 generators
negative_passages.docid: 73113
negative_passages.text: Groups and Symmetries
negative_passages.docid: 28485
negative_passages.text: Commutativity of projection and rotation
negative_passages.docid: 10908
negative_passages.text: Associated elements in a ring
negative_passages.docid: 119935
negative_passages.text: Commutator subgroup of a simple group - Fraleigh p. 152 15.19(h)
negative_passages.docid: 118117
negative_passages.text: Conjugacy Class in a matrix group with columns of standard basis
negative_passages.docid: 113357
negative_passages.text: Groups of order $pqr$ and their normal subgroups
negative_passages.docid: 108657
negative_passages.text: Cross product of the quantum mechanical operators $\textbf{p}$ and $\textbf{A}$
negative_passages.docid: 134840
negative_passages.text: Generators and relations for $\text{PSL}(2, \mathbb{F}_q)$
negative_passages.docid: 101090
negative_passages.text: Why exactly do sometimes universal covers, and sometimes central extensions feature in the application of a symmetry group to quantum physics?
negative_passages.docid: 87823
negative_passages.text: GAP: how to work with elements of the group ring of the symmetric group $\mathbb{C}[S_k]$?
negative_passages.docid: 7418
negative_passages.text: The Center of $\operatorname{GL}(n,k)$
negative_passages.docid: 142145
negative_passages.text: strictly positive elements in $C^*$-algebra
negative_passages.docid: 151009
negative_passages.text: semigroup in which Green's relations are different
negative_passages.docid: 139218
negative_passages.text: Is this group solvable?
negative_passages.docid: 80273
negative_passages.text: Prove the centralizer of an element in group $G$ is a subgroup of $G$