Products and coproducts of groups

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Contents

1 Overview
- 1.1 Summary
2 Product construction
3 Coproduct construction
4 References

Overview

This page will deal with computing a new group based off of 2 or more existing groups. Constructing new from old, but not quotient operations

Summary

Product - Categorical product of groups
Coproduct - Categorical coproduct of groups

Product construction

Categorical product of groups/Statement

Coproduct construction

Warning:Currently in the notes phase - see Notes:Products and sums of groups

References

v • d • e Group theory

Overview of the basic and important objects of group theory - a branch of abstract algebra

Primitives	semigroup [ilmath]\supset[/ilmath] monoid [ilmath]\supset[/ilmath] group [ilmath]\supset[/ilmath] Abelian group (AKA: commutative group), group action

Morphisms	Group homomorphism, Group isomorphism

Subobjects	subgroup, normal subgroup, cosets

Important theorems	First isomorphism theorem, second isomorphism theorem, third isomorphism theorem (overview of the group isomorphism theorems)

Important groups	Symmetric group (Permutation group), Alternating group, Dihedral group, Quaternion group, Klein-4 group

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