query: The group is a product of its connected component and a discrete subgroup
positive_passages.docid: 112690
positive_passages.text: Lie Group Decomposition as Semidirect Product of Connected and Discrete Groups
negative_passages.docid: 150854
negative_passages.text: Identifying a quotient group (NBHM-$2014$)
negative_passages.docid: 12667
negative_passages.text: How many subgroups of order $n$ does $D_n$ have?
negative_passages.docid: 146760
negative_passages.text: Prove that H is a subgroup of G
negative_passages.docid: 13355
negative_passages.text: Product of elements of a finite abelian group
negative_passages.docid: 147298
negative_passages.text: How to find all subgroups of a direct product?
negative_passages.docid: 147197
negative_passages.text: Number of connected components of the complement of a compact
negative_passages.docid: 103866
negative_passages.text: decomposing a factor group into a direct sum of cyclic groups
negative_passages.docid: 123828
negative_passages.text: finite and infinite product of discrete space
negative_passages.docid: 99346
negative_passages.text: Prove a result on transitive group actions.
negative_passages.docid: 80976
negative_passages.text: Direct Product Of Abelian Group
negative_passages.docid: 129830
negative_passages.text: A group with no proper non-trivial subgroups
negative_passages.docid: 29717
negative_passages.text: Not sure how to go about this group theory proof
negative_passages.docid: 132127
negative_passages.text: Proving a direct product of groups is a group
negative_passages.docid: 71245
negative_passages.text: $2 \times 2 $ Orthogonal Group
negative_passages.docid: 68955
negative_passages.text: Characterising subgroups of Prüfer $p$-groups.
negative_passages.docid: 38687
negative_passages.text: Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$