4 papers
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…
Orbit-blocking words and the average-case complexity of Whitehead's problem in the free group of rank 2
Lucy Hyde, Siobhan O'Connor, Vladimir Shpilrain
Let F_2 denote the free group of rank 2. Our main technical result of independent interest is: for any element u of F_2, there is g in F_2 such that no cyclically reduced image of…