query: Does a finite group has subgroups of order of all divisors of its order?
positive_passages.docid: 14611
positive_passages.text: $A_4$ has no subgroup of order $6$?
negative_passages.docid: 6189
negative_passages.text: Examples of infinite groups such that all their respective elements are of finite order.
negative_passages.docid: 61550
negative_passages.text: Existence of elements of order $p^k$ in a finite group
negative_passages.docid: 98734
negative_passages.text: Order of a product of elements in a generic group
negative_passages.docid: 81543
negative_passages.text: Finite abelian group contains an element with order equal to the lcm of the orders of its elements
negative_passages.docid: 15341
negative_passages.text: Non-abelian finite group in which more than half of the elements have order $2$
negative_passages.docid: 61391
negative_passages.text: Which finite groups are the group of units of some ring?
negative_passages.docid: 112993
negative_passages.text: Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
negative_passages.docid: 51352
negative_passages.text: Subgroups of a finite abelian group
negative_passages.docid: 121423
negative_passages.text: Prove that every element of a finite group has an order
negative_passages.docid: 145127
negative_passages.text: For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
negative_passages.docid: 91966
negative_passages.text: Find all subgroups of group
negative_passages.docid: 123796
negative_passages.text: Order of automorphism group of a $p$-group is divisible by $p$.
negative_passages.docid: 43750
negative_passages.text: Subgroups of finite solvable groups. Solvable?
negative_passages.docid: 83710
negative_passages.text: Order of a homomorphism of groups
negative_passages.docid: 126113
negative_passages.text: Prove the existence of order 4 subgroups of order 8 groups
negative_passages.docid: 103423
negative_passages.text: Normal subgroup where G has order prime