query: If $G$ is a finite group s.t. $|G|=4$, is it abelian ?
positive_passages.docid: 74586
positive_passages.text: Prove that every group of order $4$ is abelian
negative_passages.docid: 59007
negative_passages.text: Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
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: 66510
negative_passages.text: A group is abelian if and only if the center of the group is all the group
negative_passages.docid: 1364
negative_passages.text: Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
negative_passages.docid: 59128
negative_passages.text: If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
negative_passages.docid: 60075
negative_passages.text: Does there exist an $n$ such that all groups of order $n$ are Abelian?
negative_passages.docid: 100605
negative_passages.text: let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
negative_passages.docid: 4838
negative_passages.text: For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
negative_passages.docid: 101602
negative_passages.text: consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order 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: 142375
negative_passages.text: Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
negative_passages.docid: 43783
negative_passages.text: Abelian group (Commutative group)
negative_passages.docid: 150199
negative_passages.text: How to prove for a finite group that $|\langle g \rangle|=o(g)$?
negative_passages.docid: 36887
negative_passages.text: Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.
negative_passages.docid: 46342
negative_passages.text: Prove that $G$ is abelian iff $\varphi(g) = g^2$ is a homomorphism
negative_passages.docid: 139100
negative_passages.text: A question on the group algebra $k[G]$ of a finite abelian group