query: Showing that $g$ is a generator of $G$ implies $\phi(g)$ is a generator of $G'$.
positive_passages.docid: 144065
positive_passages.text: Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
negative_passages.docid: 95240
negative_passages.text: Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
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: 150199
negative_passages.text: How to prove for a finite group that $|\langle g \rangle|=o(g)$?
negative_passages.docid: 110708
negative_passages.text: On proving that a finitely generated group has a finite number of subgroups with index $n$.
negative_passages.docid: 46260
negative_passages.text: Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
negative_passages.docid: 124844
negative_passages.text: Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
negative_passages.docid: 130081
negative_passages.text: Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
negative_passages.docid: 95976
negative_passages.text: Given a PRF $F$ , is $G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$ a PRG?
negative_passages.docid: 63359
negative_passages.text: Show that the product of all group elements is $e$ or $u$ if $G$ has exactly one involution $u$
negative_passages.docid: 123967
negative_passages.text: Proof of a generating functions formula
negative_passages.docid: 107716
negative_passages.text: Show that $G$ is cyclic
negative_passages.docid: 58663
negative_passages.text: How to show that if $\phi(n)$ equals to n itself, then n must be 1?
negative_passages.docid: 96680
negative_passages.text: Generators of symmetric group $S_n$
negative_passages.docid: 46863
negative_passages.text: Show that $g$ is injective
negative_passages.docid: 11003
negative_passages.text: Proving that $G/N$ is an abelian group
negative_passages.docid: 62879
negative_passages.text: Question about the proof of $GCH$ holds in $\mathbf L$