Group theory is a formal method for analysing, in terms of symmetry groups, abstract and physical systems in which symmetry is present. For example, group theory classifies regular polyhedra, crystal ...

Research in group theory has long embraced equations as a means to elucidate the structure and behaviour of groups. In particular, Diophantine problems—those surrounding the existence and ...

In this paper, we show that the free solvable groups (as well as the free nilpotent groups) of finite rank have different elementary theories (i.e., they do not satisfy the same first order sentences ...

Just a short piece. A lot of people dont fully understand what a scientist means by using the word THEORY. Please see below some definitions of the word THEORY. 1. A set of statements or principles ...