English

An element of order 4 in the Nottingham group at the prime 2

Group Theory 2010-09-28 v1 Number Theory

Abstract

For k a field of characteristic 2, we show that there is a unique continuous automorphism of order 4 of the power series ring k[[t]] which sends t to t + t^2 + (t^6) + (t^{12} + t^{14}) + (t^{24} + t^{26} + t^{28} + t^{30}) + ... . For j >= 0, the j-th sum in parentheses has 2^j terms beginning at t^{6*2^j}, with successive terms in the j-th sum raising the exponent of t by 2.

Keywords

Cite

@article{arxiv.1009.5135,
  title  = {An element of order 4 in the Nottingham group at the prime 2},
  author = {Ted Chinburg and Peter Symonds},
  journal= {arXiv preprint arXiv:1009.5135},
  year   = {2010}
}