query: Prove that every element of G is a square
positive_passages.docid: 147398
positive_passages.text: If every element of $H$ and $G/H$ is a square, then prove that so is every element of $G$.
negative_passages.docid: 125702
negative_passages.text: There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
negative_passages.docid: 46674
negative_passages.text: How can I prove that every group of $N = 255$ elements is commutative?
negative_passages.docid: 4776
negative_passages.text: Prove that the power set of an $n$-element set contains $2^n$ elements
negative_passages.docid: 94507
negative_passages.text: Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
negative_passages.docid: 80273
negative_passages.text: Prove the centralizer of an element in group $G$ is a subgroup of $G$
negative_passages.docid: 90076
negative_passages.text: Prove that every positive integer $n$ is a unique product of a square and a squarefree number
negative_passages.docid: 75473
negative_passages.text: If a group $G$ has odd order, then the square function is injective.
negative_passages.docid: 74586
negative_passages.text: Prove that every group of order $4$ is abelian
negative_passages.docid: 73391
negative_passages.text: Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
negative_passages.docid: 134
negative_passages.text: Prove that the expression is a perfect square
negative_passages.docid: 59561
negative_passages.text: Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
negative_passages.docid: 41977
negative_passages.text: If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
negative_passages.docid: 58251
negative_passages.text: To show every sylow p-subgroup is normal in G
negative_passages.docid: 11003
negative_passages.text: Proving that $G/N$ is an abelian group
negative_passages.docid: 9146
negative_passages.text: Proving that a list of perfect square numbers is complete
negative_passages.docid: 143540
negative_passages.text: How to prove this decomposition of sum of squares?