query: Subgroup generated by all elements with odd order
positive_passages.docid: 27780
positive_passages.text: Subgroup which is generated by odd elements
negative_passages.docid: 126113
negative_passages.text: Prove the existence of order 4 subgroups of order 8 groups
negative_passages.docid: 114662
negative_passages.text: Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
negative_passages.docid: 108049
negative_passages.text: Determining the number of subgroups of $\Bbb Z_{14} \oplus \Bbb Z_{6}$
negative_passages.docid: 59898
negative_passages.text: Elementary manipulation with elements of group
negative_passages.docid: 98474
negative_passages.text: Show the existence of a certain subgroup of F2
negative_passages.docid: 12667
negative_passages.text: How many subgroups of order $n$ does $D_n$ have?
negative_passages.docid: 126771
negative_passages.text: Group element not taken to its inverse by any automorphism
negative_passages.docid: 121077
negative_passages.text: Product of all elements in finite group
negative_passages.docid: 91782
negative_passages.text: Efficiently find the generators of a cyclic 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: 116786
negative_passages.text: normal subgroups of Alternating group
negative_passages.docid: 94420
negative_passages.text: Dihedral group - elements of order $2$
negative_passages.docid: 67926
negative_passages.text: $S_n$ is generated by elements of the form $(1k)$
negative_passages.docid: 56607
negative_passages.text: gcd and order of elements of group
negative_passages.docid: 143293
negative_passages.text: Does every non-trivial subgroup of $S_9$ containing an odd permutation necessarily contain a transposition?
negative_passages.docid: 116936
negative_passages.text: Commutator subgroup and subgroup generated by square.