Séance Séminaire

Séminaire des Doctorant·e·s

Word Problem and Automatic Group

One question we may ask when studying a finitely generated group is whether some finite product of generators is the neutral element of the group or not. This question is known as the "word problem". In this presentation, I will introduce the notion of Group presentation and present the word problem in this context. I'll present one famous example of group type for which the word problem is solvable in an efficient way: the Automatic Groups. More precisely, given an element written as a product of generators of an Automatic Group there exists an algorithm that tells us in quadratic time if this element is the neutral element or not.