What is a semi-direct product? - Semi-direct products - Part 1

We define a complement of a subgroup N of G, then examine multiplication in G to show that an internal semi-direct product occurs as a generalization of the internal direct product.

0:00 Complements of subgroups
2:38 Internal products of groups
4:54 Internal direct product
7:15 Internal semi-direct product
9:15 Internal Zappa-Szép product

#math #maths #grouptheory

[jeromejean-charles]

Thank you : first time I understand the motivation for semidirect product. The very nice part is " let us see how multiplication works" . As questions are the heart of any matter I would have suggest to recall the question at the end of the video like "We have described how the product HK behave depending on how well behaved H and K are". Note you could also have mention that things can be done using morphisms to abstract calculations ( I agree that hands on calculations give a better grasp of the concept.

[no-one-in-particular]

Very nice, I have not seen an explanation like this elsewhere; do you have a source?