Recent content by Martin T

Saw

Yes, I understand, but in the book Arnold first defines an action: Let M be a group and M a set. We say that an action of the group G on the set M is defined if to each element g of G there corresponds a transformation Tg : M→M of the set M, to the product and inverse elements corresponds...

But if T takes m to m, how is the same which T takes g of G(or gh of G) to S(M)=group of all bijective transformations of M. And say Arnold's books are ""pedagogic".

Then it is a old fashioned notation, thanks

Yes I think the same, then Arnold is wrong with Tg:M→M.

Here the Page, the Last paragragh, thanks.

Yes, but Arnold is popular and this paragraph is being kill me.

In Arnold's book, ordinary differential equations 3rd. WHY Arnold say Tg:M→M instead of Tg:G→S(M) for transformations Tfg=Tf Tg, Tg^-1=(Tg)^-1. Let M be a group and M a set. We say that an action of the group G on the set M is defined if to each element g of G there corresponds a...

Mathematical analysis Zorich is good and well motivated

It is done. Really Thanks a lot.

Thanks your explanation was so clear , the reason of the post is If there exists the different between the action of a group and the action of a element g of a group G for example. The definition of ARTIN's book was nothing precise.

hi everyone, I'm electrical engineer student and i like a lot arnold's book of ordinary differential equations (3rd), but i have a gap about how defines action group for a group and from an element of the group.For example Artin's algebra book get another definition also Vinberg's algebra book...