query: Condition when any union of subgroups is subgroup
positive_passages.docid: 146952
positive_passages.text: When can I say that $\cup H_i$ is a group?
negative_passages.docid: 144788
negative_passages.text: Cosets of a subgroup do not overlap
negative_passages.docid: 107935
negative_passages.text: If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
negative_passages.docid: 129753
negative_passages.text: Prove that a subgroup which contains half of all elements is a normal subgroup.
negative_passages.docid: 96878
negative_passages.text: A finite group with the property that all of its proper subgroups are abelian
negative_passages.docid: 101345
negative_passages.text: Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
negative_passages.docid: 2174
negative_passages.text: Proving that HK is a subgroup when K is normal
negative_passages.docid: 154398
negative_passages.text: Show that H is a subgroup of G
negative_passages.docid: 13453
negative_passages.text: Bijection map from a set of subgroup to another set of subgroup under some condition.
negative_passages.docid: 118030
negative_passages.text: Two subgroups of the same index must be conjugate under these assumptions
negative_passages.docid: 157330
negative_passages.text: Showing the image of a subgroup is a subgroup.
negative_passages.docid: 125498
negative_passages.text: Check whether subgroup is normal in $ S_4$
negative_passages.docid: 113925
negative_passages.text: Normal Subgroup Counterexample
negative_passages.docid: 51747
negative_passages.text: Showing that the intersection of all subgroups of order $n$ is normal
negative_passages.docid: 41231
negative_passages.text: Subgroups of (Z,+) of order n
negative_passages.docid: 45580
negative_passages.text: Intersection of conjugate subgroups is normal
negative_passages.docid: 109517
negative_passages.text: A subgroup such that every left coset is contained in a right coset.