# Category:Subset Products

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This category contains results about Subset Products.

Definitions specific to this category can be found in Definitions/Subset Products.

Let $\struct {S, \circ}$ be an algebraic structure.

We can define an operation on the power set $\powerset S$ as follows:

- $\forall A, B \in \powerset S: A \circ_\mathcal P B = \set {a \circ b: a \in A, b \in B}$

This is called the **operation induced on $\powerset S$ by $\circ$**, and $A \circ_\mathcal P B$ is called the **subset product** of $A$ and $B$.

## Subcategories

This category has the following 8 subcategories, out of 8 total.

### E

### O

### P

### S

## Pages in category "Subset Products"

The following 35 pages are in this category, out of 35 total.

### I

### O

### P

- Power Set of Group under Induced Operation is Monoid
- Power Set of Group under Induced Operation is Semigroup
- Power Set of Magma under Induced Operation is Magma
- Power Set of Monoid under Induced Operation is Monoid
- Power Set of Semigroup under Induced Operation is Semigroup
- Product of Subgroup with Itself
- Product of Subset with Intersection
- Product of Subset with Union

### S

- Subgroup Subset of Subgroup Product
- Subset of Subset Product
- Subset Product Action is Group Action
- Subset Product is Subset of Generator
- Subset Product of Abelian Subgroups
- Subset Product of Normal Subgroups is Normal
- Subset Product of Subgroups
- Subset Product with Normal Subgroup as Generator
- Subset Product with Normal Subgroup is Subgroup
- Subset Product within Commutative Structure is Commutative
- Subset Product within Semigroup is Associative
- Subset Product within Semigroup is Associative/Corollary
- Subset Products of Normal Subgroup with Normal Subgroup of Subgroup
- Subset Relation is Compatible with Subset Product
- Subset Relation is Compatible with Subset Product/Corollary 1
- Subset Relation is Compatible with Subset Product/Corollary 2
- Sum of All Ring Products is Additive Subgroup