query: On direct product of groups
positive_passages.docid: 129120
positive_passages.text: Example of a group $G$ such that $G = N_1\cdots N_n$ and $N_i \cap N_j = \{e\}$ for all $i \neq j$ but $G$ is not the internal direct product of them.
negative_passages.docid: 59211
negative_passages.text: Product of Finite Abelian Group
negative_passages.docid: 80976
negative_passages.text: Direct Product Of Abelian Group
negative_passages.docid: 33294
negative_passages.text: The correspondence theorem for groups
negative_passages.docid: 98155
negative_passages.text: Free products of cyclic groups
negative_passages.docid: 37960
negative_passages.text: Zero Divisors in Direct Product of Rings
negative_passages.docid: 113259
negative_passages.text: The confusing nature of direct sum for finite abelian groups
negative_passages.docid: 73382
negative_passages.text: A concrete example of involution in group theory
negative_passages.docid: 147298
negative_passages.text: How to find all subgroups of a direct product?
negative_passages.docid: 129830
negative_passages.text: A group with no proper non-trivial subgroups
negative_passages.docid: 38687
negative_passages.text: Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$
negative_passages.docid: 81354
negative_passages.text: The product of all the elements of a finite abelian group
negative_passages.docid: 53357
negative_passages.text: Cyclic Group Generators of Order $n$
negative_passages.docid: 11957
negative_passages.text: G is the product of its Sylow subgroups
negative_passages.docid: 153092
negative_passages.text: Homology of disjoint union is direct sum of homologies
negative_passages.docid: 111049
negative_passages.text: Groups with given automorphism groups
negative_passages.docid: 71245
negative_passages.text: $2 \times 2 $ Orthogonal Group