query: How can the symmetric group $S_3$ be represented as $\{1, x, x^2, y, xy, x^2y\}$
positive_passages.docid: 107163
positive_passages.text: Proof that $S_3$ isomorphic to $D_3$
negative_passages.docid: 2064
negative_passages.text: Finite subgroups of orthogonal transformations in $\mathbb{R}^3$
negative_passages.docid: 142038
negative_passages.text: Finding the number of elements of order two in the symmetric group $S_4$
negative_passages.docid: 156247
negative_passages.text: Question about permutations and cycles (Groups and Symmetries)
negative_passages.docid: 36797
negative_passages.text: How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?
negative_passages.docid: 157806
negative_passages.text: Order of a element on a Symmetric Group
negative_passages.docid: 14895
negative_passages.text: Reference for the subgroup structure of $\rm{PSL}_2(q)$
negative_passages.docid: 72853
negative_passages.text: What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters?
negative_passages.docid: 117414
negative_passages.text: How would I prove what elements $S_3$ contains, and what its subgroups are?
negative_passages.docid: 109596
negative_passages.text: Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
negative_passages.docid: 134709
negative_passages.text: Express symmetric polynomial $\prod_{i < j} (X_i+X_j)$ in terms of elementary symmetric functions
negative_passages.docid: 136083
negative_passages.text: Show that $\sigma\circ\phi : G_1 \to G_3$ is an isomorphism
negative_passages.docid: 36137
negative_passages.text: Prove $GL_2(\mathbb{Z}/2\mathbb{Z})$ is isomorphic to $S_3$
negative_passages.docid: 121449
negative_passages.text: An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$
negative_passages.docid: 114987
negative_passages.text: How many connected components does $\mathrm{GL}_n(\mathbb R)$ have?
negative_passages.docid: 73113
negative_passages.text: Groups and Symmetries
negative_passages.docid: 21568
negative_passages.text: Maximal order of an element in a symmetric group