query: Every group of order $35$ is cyclic?
positive_passages.docid: 151025
positive_passages.text: If G is a group of order n=35, then it is cyclic
negative_passages.docid: 147517
negative_passages.text: Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
negative_passages.docid: 8746
negative_passages.text: Groups of order $pq$ without using Sylow theorems
negative_passages.docid: 46674
negative_passages.text: How can I prove that every group of $N = 255$ elements is commutative?
negative_passages.docid: 16259
negative_passages.text: How many non isomorphic groups of order 30 are there?
negative_passages.docid: 14528
negative_passages.text: Proof that all abelian simple groups are cyclic groups of prime order
negative_passages.docid: 158074
negative_passages.text: Cyclic group $G$ with generator $ab$.
negative_passages.docid: 104460
negative_passages.text: When a group is cyclic
negative_passages.docid: 107716
negative_passages.text: Show that $G$ is cyclic
negative_passages.docid: 91782
negative_passages.text: Efficiently find the generators of a cyclic group
negative_passages.docid: 53357
negative_passages.text: Cyclic Group Generators of Order $n$
negative_passages.docid: 2304
negative_passages.text: What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
negative_passages.docid: 89508
negative_passages.text: Existence of normal subgroups for a group of order $36$
negative_passages.docid: 8623
negative_passages.text: Finite subgroups of the multiplicative group of a field are cyclic
negative_passages.docid: 36887
negative_passages.text: Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.
negative_passages.docid: 53207
negative_passages.text: Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
negative_passages.docid: 129061
negative_passages.text: How to say that any group of order $pqr$ is cyclic with a provided relation between $p$, $q$, $r$, where they are all distinct primes.