ON THE WORD AND PERIOD GROWTH OF SOME GROUPS OF TREE AUTOMORPHISMS

Abstract

We generalize a class of groups defined by Rostislav Grigorchuk in [Gri84] to a much larger class of groups, and provide upper and lower bounds for their word growth (they are all of intermediate growth) and period growth.

ACKNOWLEDGMENTS

Both authors are thankful to Pierre de la Harpe and Rostislav Grigorchuk for their support, useful suggestions and guidance through the subject.

In addition, the second author would like to express gratitude to his advisor Fernando Guzmán for providing infinite listening patience, encouragement and plenty of good ideas. Also, thanks to Matthew Brin for a partial introduction to the subject.

The first author expresses his thanks to the “Swiss National Science Foundation”