Two problems about subgroups of free groups concerning the lengths of their generators
Lucy Koch-Hyde, Éamonn Olive
Abstract
We will answer a problem of Dotsenko that asks for a tight upper bound on the rank of subgroups given a maximum length for its generators. Then, we will use the same tools to answer a longstanding problem of Grigorchuk in the 10th edition of the Kourovka notebook. We accomplish this using Stallings foldings and simple graph theory.
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