Poincare group (the first fundamental group) of equivalent or homotopic topological spaces are isomorphic. The same for higher dimensional fundamental groups of the topological spaces.

Hope the attached paper is helpful to follow the commutator

of the essential groups of Poincare and Lorentz.

Poincare group (the first fundamental group) of equivalent or homotopic topological spaces are isomorphic. The same for higher dimensional fundamental groups of the topological spaces.

Hope the attached paper is helpful to follow the commutator

of the essential groups of Poincare and Lorentz.

may be help of your attached link and attachment friend

https://www.jstor.org/stable/2372559?seq=1#page_scan_tab_contents

Thanks for the links, but I would like to narrow the discussion and discuss the issue of the possibility of generating some groups by others by means of the automorphism of a factorized integer lattice.