Category:Quotient Groups
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This category contains results about Quotient Groups.
Definitions specific to this category can be found in Definitions/Quotient Groups.
Let $G$ be a group.
Let $N$ be a normal subgroup of $G$.
Then the left coset space $G / N$ is a group, where the group operation is defined as the coset product:
- $\paren {a N} \paren {b N} = \paren {a b} N$
$G / N$ is called the quotient group of $G$ by $N$.
Subcategories
This category has the following 11 subcategories, out of 11 total.
Pages in category "Quotient Groups"
The following 42 pages are in this category, out of 42 total.
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- Quotient Epimorphism is Epimorphism/Group
- Quotient Group by Intersection of Normal Subgroups not necessarily Cyclic if Quotient Groups are
- Quotient Group is Abelian iff All Commutators in Divisor
- Quotient Group is Group
- Quotient Group is Group/Corollary
- Quotient Group is Subgroup of Power Structure of Group
- Quotient Group of Abelian Group is Abelian
- Quotient Group of Cyclic Group
- Quotient Group of Direct Products
- Quotient Group of Ideal is Coset Space
- Quotient Group of Infinite Cyclic Group by Subgroup
- Quotient Group of Solvable Group is Solvable
- Quotient of Group by Center Cyclic implies Abelian
- Quotient of Sylow P-Subgroup
- Quotient of Transformation Group acts Effectively
- Quotient Theorem for Group Epimorphisms
- Quotient Theorem for Group Homomorphisms
- Quotient Theorem for Group Homomorphisms/Corollary 1
- Quotient Theorem for Group Homomorphisms/Corollary 2