query: Proving a semidirect product of two groups is isomorphic to the direct product of the same groups
positive_passages.docid: 156909
positive_passages.text: $\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.
negative_passages.docid: 146969
negative_passages.text: Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
negative_passages.docid: 5741
negative_passages.text: Direct product of abelian groups
negative_passages.docid: 91997
negative_passages.text: Product of two subgroups the whole group?
negative_passages.docid: 84869
negative_passages.text: Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
negative_passages.docid: 70688
negative_passages.text: How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
negative_passages.docid: 114916
negative_passages.text: $\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
negative_passages.docid: 88928
negative_passages.text: $F:G\to B$ is an isomorphism between groups implies $F^{-1}$ is an isomorphism
negative_passages.docid: 55393
negative_passages.text: Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
negative_passages.docid: 72295
negative_passages.text: A difficulty in understanding the proof of distributivity of tensor products over direct sums for modules.
negative_passages.docid: 16476
negative_passages.text: Order of the product of two commuting elements with coprime orders in a group.
negative_passages.docid: 157915
negative_passages.text: Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
negative_passages.docid: 42096
negative_passages.text: Direct product of Sylow subgroups
negative_passages.docid: 120155
negative_passages.text: How to show that this group presentation is isomorphic to dihedral group?
negative_passages.docid: 112690
negative_passages.text: Lie Group Decomposition as Semidirect Product of Connected and Discrete Groups
negative_passages.docid: 151862
negative_passages.text: Is any subgroup of a direct product isomorphic to a direct product of subgroups?
negative_passages.docid: 120288
negative_passages.text: Semigroup isomorphism