query: Finite group of odd order with elements that are square
positive_passages.docid: 121929
positive_passages.text: What finite groups always have a square root for each element?
negative_passages.docid: 148904
negative_passages.text: Groups of order $p^3$
negative_passages.docid: 85106
negative_passages.text: Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
negative_passages.docid: 13355
negative_passages.text: Product of elements of a finite abelian group
negative_passages.docid: 60982
negative_passages.text: Group where every element is order 2
negative_passages.docid: 15526
negative_passages.text: Question on groups of order $pq$
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: 67554
negative_passages.text: In a group, the number of non-self-inverse elements is even
negative_passages.docid: 122125
negative_passages.text: Order of group element divides order of finite group
negative_passages.docid: 59811
negative_passages.text: Finite Abelian groups with the same number of elements for all orders are isomorphic
negative_passages.docid: 64269
negative_passages.text: Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
negative_passages.docid: 134676
negative_passages.text: Number of elements of order $p$ is a multiple of $p-1$ (finite group).
negative_passages.docid: 92750
negative_passages.text: Groups where all elements are order 3
negative_passages.docid: 108309
negative_passages.text: An example of a non-abelian group of order $p^3$
negative_passages.docid: 72767
negative_passages.text: Center of the dihedral group with odd and even number of vertices
negative_passages.docid: 156319
negative_passages.text: Show that a group with $|G| = 33$ contains an element of order $3$
negative_passages.docid: 26398
negative_passages.text: Group of even order contains an element of order 2