semi_direct_product

introduction

%%visits: 2 The semi_direct_product is used to decompose large groups into smaller groups, and hopefully find the [[normal_subgroup]]s of the groups too, to really understand what is going on with these objects and therefore learning more about operations, elements and different interactions between two numbers.

The motivation for the semi_direct_product is to give only 1 normal subgroup

intuition

There are different notation to the semi_direct_product. ⋉ = ⊳ + ×

And J = G ⋉ H is called an extension of H by G ## rigour The semi_direct_produc := The set H × G with the group operation. (g₁, h₁)(g₂, h₂) = (g₁g₂, g₁ϕ_g1(h₂) ## exam clinic ## examples and non-examples ## resources tags :math:

backlinks

• index_of_files.pd