Commutators and squares in free groups
Sucharit Sarkar
Abstract
Let F2 be the free group generated by x and y. In this article, we prove that the commutator of xm and yn is a product of two squares if and only if mn is even. We also show using topological methods that there are infinitely many obstructions for an element in F2 to be a product of two squares.
Create a lesson
Related papers
The variety generated by all additively idempotent semirings of order four
Mengya Yue, Xiaolei Shao
Generation of Iterated Wreath Products Constructed from Full Transformation Monoids and Symmetric Groups
Jiaping Lu
Kernel--wreath constructions and infinite families of finite simple skew braces
Marco Damele
Explicit equational bases for the power semirings of S7
Mengya Yue, Miaomiao Ren, Zidong Gao
The free multiplicative Lie algebra L(P) for a finitely generated parafree group P
Dessislava H. Kochloukova
An order automorphism of a Dlab group not induced by conjugation
Ting Gong, Yong Yang, Michael Ruofan Zeng