query: Finite order In a non-abelian group
positive_passages.docid: 8742
positive_passages.text: Examples and further results about the order of the product of two elements in a group
negative_passages.docid: 85579
negative_passages.text: $G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
negative_passages.docid: 122125
negative_passages.text: Order of group element divides order of finite group
negative_passages.docid: 88344
negative_passages.text: Order of a group and subsequent subgroups
negative_passages.docid: 63499
negative_passages.text: Groups of prime squared order
negative_passages.docid: 41688
negative_passages.text: An elementary problem in Group Theory: the unique noncyclic group of order 4
negative_passages.docid: 100061
negative_passages.text: The Maximum possible order for an element $S_n$
negative_passages.docid: 99309
negative_passages.text: Groups of order $n^2$ that have no subgroup of order $n$
negative_passages.docid: 56607
negative_passages.text: gcd and order of elements of group
negative_passages.docid: 55719
negative_passages.text: Order of general- and special linear groups over finite fields.
negative_passages.docid: 84789
negative_passages.text: Order of products of elements in a finite Abelian group
negative_passages.docid: 67554
negative_passages.text: In a group, the number of non-self-inverse elements is even
negative_passages.docid: 16476
negative_passages.text: Order of the product of two commuting elements with coprime orders in a group.
negative_passages.docid: 150760
negative_passages.text: Are there any distinct finite simple groups with the same order?
negative_passages.docid: 131204
negative_passages.text: A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
negative_passages.docid: 128692
negative_passages.text: Example of an infinite group where every element except identity has order 2
negative_passages.docid: 75590
negative_passages.text: How many normal subgroups does a non-abelian group $G$ of order $ 21$