query: If I know the order of every element in a group, do I know the group?
positive_passages.docid: 28676
positive_passages.text: Is a finite group uniquely determined by the orders of its elements?
negative_passages.docid: 42469
negative_passages.text: Find all groups of order $6$.
negative_passages.docid: 114535
negative_passages.text: what groups have only elements of prime order?
negative_passages.docid: 13153
negative_passages.text: at least one element fixed by all the group
negative_passages.docid: 88344
negative_passages.text: Order of a group and subsequent subgroups
negative_passages.docid: 59898
negative_passages.text: Elementary manipulation with elements of group
negative_passages.docid: 141379
negative_passages.text: All groups where underlying set has at most 4 elements
negative_passages.docid: 33819
negative_passages.text: What does "the ${\bf N}$ of a group" mean?
negative_passages.docid: 114187
negative_passages.text: In a finite cyclic group, the generator has the order of the group
negative_passages.docid: 142718
negative_passages.text: How can I find the smallest set of groups of $n$ elements such that every element is in the same group as every other at least once?
negative_passages.docid: 124224
negative_passages.text: How many groups of order $n$ with center {e} exist?
negative_passages.docid: 62255
negative_passages.text: Notation question: Subroup generated by two elements?
negative_passages.docid: 56607
negative_passages.text: gcd and order of elements of group
negative_passages.docid: 84789
negative_passages.text: Order of products of elements in a finite Abelian group
negative_passages.docid: 128544
negative_passages.text: What are the subcategories of ordered sets / groups?
negative_passages.docid: 19668
negative_passages.text: Does every group whose order is a power of a prime p contain an element of order p?
negative_passages.docid: 38083
negative_passages.text: Order of conjugate of an element given the order of its conjugate