Small cancellation theory over Burnside groups
Résumé
We develop a theory of small cancellation theory in the variety of Burnside groups. More precisely, we show that there exists a critical exponent $n_0$ such that for every odd $n\geq n_0$, the well-known classical $C'(1/6)$-small cancellation theory, as well as its graphical generalization and its version for free products, produce examples of infinite $n$-periodic groups. Our result gives a powerful tool for producing (uncountable collections of) examples of periodic groups with prescribed properties. It can be applied without any prior knowledge in the subject of periodic groups. As applications, we show the undecidability of Markov properties in classes of periodic groups, we produce periodic groups with expander graphs embedded in their Cayley graphs, and we give an $n$-periodic Rips construction. We also obtain simpler proofs of the known results like the existence of uncountably many finitely generated periodic groups and the SQ-universality (in the class of periodic groups) of free Burnside groups.
Domaines
Théorie des groupes [math.GR]
Origine : Fichiers produits par l'(les) auteur(s)