Category:Group Direct Products
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This category contains results about Group Direct Products.
Definitions specific to this category can be found in Definitions/Group Direct Products.
Let $\struct {G, \circ_1}$ and $\struct {H, \circ_2}$ be groups.
Let $G \times H: \set {\tuple {g, h}: g \in G, h \in H}$ be their cartesian product.
The (external) direct product of $\struct {G, \circ_1}$ and $\struct {H, \circ_2}$ is the group $\struct {G \times H, \circ}$ where the operation $\circ$ is defined as:
- $\tuple {g_1, h_1} \circ \tuple {g_2, h_2} = \tuple {g_1 \circ_1 g_2, h_1 \circ_2 h_2}$
This is usually referred to as the group direct product of $G$ and $H$.
Subcategories
This category has the following 12 subcategories, out of 12 total.
D
- Direct Sums of Rings (2 P)
I
Pages in category "Group Direct Products"
The following 36 pages are in this category, out of 36 total.
A
C
D
- Direct Product of Central Subgroups
- Direct Product of Group Homomorphisms is Homomorphism
- Direct Product of Normal Subgroups is Normal
- Direct Product of Solvable Groups is Solvable
- Direct Product of Sylow p-Subgroups is Sylow p-Subgroup
- Direct Product of Unique Sylow p-Subgroups is Unique Sylow p-Subgroup