query: Only two groups of order 10.
positive_passages.docid: 24970
positive_passages.text: Only two groups of order $10$: $C_{10}$ and $D_{10}$
negative_passages.docid: 79995
negative_passages.text: G is group of order pq, pq are primes
negative_passages.docid: 49366
negative_passages.text: Group of order 30 can't be simple
negative_passages.docid: 81892
negative_passages.text: Find four groups of order 20 not isomorphic to each other.
negative_passages.docid: 95196
negative_passages.text: No simple group of order $300$
negative_passages.docid: 80381
negative_passages.text: Groups with "few" subgroups
negative_passages.docid: 14263
negative_passages.text: Ordering problem
negative_passages.docid: 79380
negative_passages.text: How to find the order of a group generated by two elements?
negative_passages.docid: 41731
negative_passages.text: Question about the order of the product of two elements in an abelian group
negative_passages.docid: 8742
negative_passages.text: Examples and further results about the order of the product of two elements in a group
negative_passages.docid: 93286
negative_passages.text: There are $10$ commutative rings of order $8$
negative_passages.docid: 51196
negative_passages.text: A group of order $p^2q^2$ is never simple
negative_passages.docid: 14611
negative_passages.text: $A_4$ has no subgroup of order $6$?
negative_passages.docid: 108309
negative_passages.text: An example of a non-abelian group of order $p^3$
negative_passages.docid: 123560
negative_passages.text: Intuition behind why order of a subgroup divides order of a group.
negative_passages.docid: 149030
negative_passages.text: Nonisomorphic groups of order 12.
negative_passages.docid: 93760
negative_passages.text: There is an element of order $51$ in the multiplicative group $(Z/103Z)^∗.$