query: Why is not Z/pqZ* cyclic?
positive_passages.docid: 28644
positive_passages.text: For $q, p$ odd primes such that $p \neq q$, there is not primitive root modulo $pq$.
negative_passages.docid: 110808
negative_passages.text: Isomorphisms preserve cyclic
negative_passages.docid: 127306
negative_passages.text: Is the group of units of a finite ring cyclic?
negative_passages.docid: 56745
negative_passages.text: Why does this not work with an imaginary exponent?
negative_passages.docid: 33300
negative_passages.text: Showing order of $Z (G) =1$ or $pq$
negative_passages.docid: 117178
negative_passages.text: Cyclic group generators
negative_passages.docid: 25744
negative_passages.text: Multiplication in Permutation Groups Written in Cyclic Notation
negative_passages.docid: 128711
negative_passages.text: $(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
negative_passages.docid: 24351
negative_passages.text: The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
negative_passages.docid: 135524
negative_passages.text: Is $\mathrm{ZFC}^E$ outright inconsistent?
negative_passages.docid: 132725
negative_passages.text: Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
negative_passages.docid: 26764
negative_passages.text: Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
negative_passages.docid: 53335
negative_passages.text: Why isn't $\mathbb{C}[x,y,z]/(xz-y)$ a flat $\mathbb{C}[x,y]$-module
negative_passages.docid: 124455
negative_passages.text: Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
negative_passages.docid: 63300
negative_passages.text: Product of Consecutive Integers is Not a Power
negative_passages.docid: 75970
negative_passages.text: $\mathbb Z[1/2]$ is not finitely generated?
negative_passages.docid: 117484
negative_passages.text: Why is $c+q$ still a primitive root modulo $q$?