The Wolfram axiom is the result of a computer exploration undertaken by Stephen Wolfram in his A New Kind of Science looking for the shortest single axiom equivalent to the axioms of Boolean algebra (or propositional calculus). The result of his search was an axiom with six Nand's and three variables equivalent to Boolean algebra:
((a.b).c).(a.((a.c).a)) = c
With the dot representing the Nand logical operation (also known as the Sheffer stroke), with the following meaning: p Nand q is true if and only if not both p and q are true. It is named for Henry M. Sheffer, who proved that all the usual...
let $G$ be a group such that $Aut(G)$ is abelian. is then $G$ abelian?
this is a sort of generalization of the well-known exercise, that $G$ is abelian when $Aut(G)$ is cyclic. but I have no idea. at least, the finitely generated abelian groups $G$ such that $Aut(G)$ is abelian can be classified.
