query: A finite group of even order has an odd number of elements of order 2
positive_passages.docid: 26398
positive_passages.text: Group of even order contains an element of order 2
negative_passages.docid: 107010
negative_passages.text: How many elements of order $k$ are in $S_n$?
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: 63798
negative_passages.text: How can you show there are only 2 nonabelian groups of order 8?
negative_passages.docid: 13355
negative_passages.text: Product of elements of a finite abelian group
negative_passages.docid: 115973
negative_passages.text: Computing the number of nonisomorphic finite abelian groups of order $n$
negative_passages.docid: 27780
negative_passages.text: Subgroup which is generated by odd elements
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: 141188
negative_passages.text: Groups of order $56$
negative_passages.docid: 85579
negative_passages.text: $G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
negative_passages.docid: 79055
negative_passages.text: Orders of a symmetric group
negative_passages.docid: 104112
negative_passages.text: Number of finite simple groups of given order is at most $2$ - is a classification-free proof possible?
negative_passages.docid: 88718
negative_passages.text: A group is generated by two elements of order $2$ is infinite and non-abelian
negative_passages.docid: 53409
negative_passages.text: Show group of order $4n + 2$ has a subgroup of index 2.
negative_passages.docid: 46940
negative_passages.text: On Groups of Order 315 with a unique sylow 3-subgroup .
negative_passages.docid: 60982
negative_passages.text: Group where every element is order 2
negative_passages.docid: 52121
negative_passages.text: Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.