query: Show that if $G$ is Hamiltonian, then $L(G)$ is Hamiltonian.
positive_passages.docid: 20544
positive_passages.text: Proving that if $G$ has a Hamiltonian circuit, then the line graph $L(G)$ also has a Hamiltonian Circuit
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: 29996
negative_passages.text: Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
negative_passages.docid: 26658
negative_passages.text: A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.
negative_passages.docid: 77221
negative_passages.text: Prove that $G$ has a subgroup isomorphic to $G/H$.
negative_passages.docid: 111703
negative_passages.text: If $H \leq G$ and $[G:H]! \leq |G|$ then $G$ is not simple
negative_passages.docid: 22477
negative_passages.text: If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
negative_passages.docid: 95686
negative_passages.text: $Lie(G \times H)\cong Lie(G)\oplus Lie(H)$
negative_passages.docid: 105666
negative_passages.text: What's an easy way to show that $GL(n,\mathbb C)$ is connected?
negative_passages.docid: 83273
negative_passages.text: Show that $o(gHg^{-1})=o(H)$
negative_passages.docid: 59561
negative_passages.text: Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
negative_passages.docid: 86823
negative_passages.text: proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
negative_passages.docid: 46053
negative_passages.text: How to find Hamiltonian from this simple Lagrangian? (tricky)
negative_passages.docid: 143095
negative_passages.text: If an $H\le G$ has an irreducible representation of dimension $d$, then show $G$ has an irreducible representation of at least dimension $d$.
negative_passages.docid: 78182
negative_passages.text: Hamiltonian or not?
negative_passages.docid: 71420
negative_passages.text: Prove that a group is abelian.
negative_passages.docid: 107716
negative_passages.text: Show that $G$ is cyclic