Canonical Description of Group Theory: A Linear Order on All Finite Groups
Juan Pablo Ramírez · Preprints.org · 2020
We provide a construction of natural numbers that is unique with respect to other constructions, and use this construction in the domain of algebra and finite functions to find several results in finite group theory. First, we give a linear order to the set of all finite functions. This gives a linear order in the subset of all finite permutations. To do this, we assign a unique natural number, $N_f$, to every finite function $f$. The sub order on permutations is well defined with respect to cardinality; if $\eta_m,\eta_n$ are permutations on $m