query: Is there any condition for groups that have subgroups of order of all divisors of its order?
positive_passages.docid: 18181
positive_passages.text: Complete classification of the groups for which converse of Lagrange's Theorem holds
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: 156941
negative_passages.text: Subgroups of $\mathbb{Z}$
negative_passages.docid: 129830
negative_passages.text: A group with no proper non-trivial subgroups
negative_passages.docid: 66510
negative_passages.text: A group is abelian if and only if the center of the group is all the group
negative_passages.docid: 51352
negative_passages.text: Subgroups of a finite abelian group
negative_passages.docid: 68201
negative_passages.text: Cyclic group of order $n$
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: 123796
negative_passages.text: Order of automorphism group of a $p$-group is divisible by $p$.
negative_passages.docid: 9393
negative_passages.text: Order of elements is lcm-closed in abelian groups
negative_passages.docid: 114535
negative_passages.text: what groups have only elements of prime order?
negative_passages.docid: 13807
negative_passages.text: Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S
negative_passages.docid: 117899
negative_passages.text: At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
negative_passages.docid: 113357
negative_passages.text: Groups of order $pqr$ and their normal subgroups
negative_passages.docid: 40513
negative_passages.text: A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
negative_passages.docid: 15526
negative_passages.text: Question on groups of order $pq$
negative_passages.docid: 96878
negative_passages.text: A finite group with the property that all of its proper subgroups are abelian