query: Union subgroup implies that the group is one of the subgroups.
positive_passages.docid: 13059
positive_passages.text: If a group is the union of two subgroups, is one subgroup the group itself?
negative_passages.docid: 70034
negative_passages.text: Showing that this set of functions is a group.
negative_passages.docid: 36709
negative_passages.text: subgroup of direct product of two groups
negative_passages.docid: 154398
negative_passages.text: Show that H is a subgroup of G
negative_passages.docid: 102912
negative_passages.text: Subgroups of finitely generated groups are not necessarily finitely generated
negative_passages.docid: 42389
negative_passages.text: If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
negative_passages.docid: 138406
negative_passages.text: If N and every subgroup of N is normal in G then G/N is abelian .
negative_passages.docid: 129485
negative_passages.text: A subgroup of a cyclic group is cyclic - Understanding Proof
negative_passages.docid: 28108
negative_passages.text: Proving the kernel is a normal subgroup.
negative_passages.docid: 23533
negative_passages.text: All subgroups normal $\implies$ abelian group
negative_passages.docid: 139096
negative_passages.text: $|AxA|$ is a constant implies normal subgroup
negative_passages.docid: 44152
negative_passages.text: If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
negative_passages.docid: 138297
negative_passages.text: Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
negative_passages.docid: 146760
negative_passages.text: Prove that H is a subgroup of G
negative_passages.docid: 2174
negative_passages.text: Proving that HK is a subgroup when K is normal
negative_passages.docid: 17510
negative_passages.text: Proving a set is an abelian group.
negative_passages.docid: 85508
negative_passages.text: Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.