Sure they do, I even gave you the line and paragraph in the Moller book.
I have also pointed out to both you and przyk that, contrary to your claims, the Lorentz transforms satisfy that condition and both of you came back with some very lame answers.
Then it appears you are not only apathetic for not reading what I said but you're also unable to do basic calculus. In a specific representation the Lorentz transforms can satisfy $$\Lambda \cdot \Lambda^{\top} = I$$ but not in all represnetations. You made a general statement, which is false. The standard representation of Lorentz transformations don't satisfy them.
This seems to be your standard mistake, you make broad statements which are infact only true for particular cases. You did it for Christoffel symbols too.
Then there's Guest's example, $$(x,y) = (R\cos t,R\sin t)$$. If $$JJ^{\top}=I$$ then det(J) = $$\pm 1$$. The determinant of the Jacobian of that example has determinant R (or 1/R, depending which way you're going). No representation is going to satisfy $$JJ^{\top}=I$$ for general R.
Its trivial to construct such counter examples. For instance, $$(x')^{a} = \lambda x^{a}$$ in $$\mathbb{R}^{N}$$ will have a Jacobian determinant of $$\lambda^{N}$$. If $$\lambda \neq 1$$ (or zero, to be valid) then its a counterexample to your claim.
You clearly fail to realise the book you're reading is talking about specific cases, not all cases.
I read your posts, I am tired on your harping on the same nonsense so I gave you a little challenge that should have taken you 5 minutes to complete. You have been posting for 1.5 hours but nothing on the challenge.
Yes, you're tired of me harping on about your mistakes so you're trying to make up an excuse to ignore me. Can I be bothered to do your little challenge? No. Does that mean your mistakes are not mistakes? No.
I am not changing the subject, I am just tired about your regurgitating the same stuff, so I decided to post a challenge. We can work in parallel, I will answer to your tripe while you are still struggling with answering my challenge.
I don't need to prove myself by jumping through your hoops. Do you think I'm unfamiliar with coordinate transforms, Jacobians, covariance etc? If you're Trout from PhysOrg then you know I'm more than capable when it comes to those things, so your "Why don't you do my challenge!" is just an excuse to avoid facing up to your mistakes.
Given your mistakes when it comes to covariance, Jacobians and coordinate transforms I seriously wonder if you can even do such things. If you're the person banned from editing Wikipedia Guest linked to then clearly I'm not the first person to have misgivings about your abilities.
Then you should not be posting in this thread. This thread is about Shubert's theory. Post elsewhere and I will answer your questions.
So no one should ever point out a mistake in someone's post if that mistake isn't directly to do with the original post? Oh please.
The reason this thread is so off topic is because
you couldn't just say "Fair point, I was mistaken about that". Instead it takes 4 or 5 pages of several people explaining your mistake half a dozen different ways before you realise you're wrong and then you try to change the subject. If you'd just faced up to your mistake there'd have been no need to reiterate it again and again.