4 papers
Two problems about bases and independent sets in free groups
Lucy Koch-Hyde, Éamonn Olive
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 answe…
More Residually Solvable One-Relator Groups
Lucy Koch-Hyde, Siobhan O'Connor, Eamonn Olive
We say a word in a free group is ``partially positive'' if there is at least one generator which appears in the word, but does not appear with negative exponent. We show that one-r…
Growth and Language Complexity of Potentially Positive Elements of Free Groups
Emma Dinowitz, Lucy Koch-Hyde, Siobhan O'Connor +1
A word in a free group is called ``potentially positive'' if it is automorphic to an element which is written with only positive exponents. We will develop automata to analyze prop…
Orbit-blocking words in free groups
Lucy Koch-Hyde, Siobhan O'Connor, Eamonn Olive +1
By strengthening known results about primitivity-blocking words in free groups, we prove that for any nontrivial element w of a free group of finite rank, there are words that cann…