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On the Laxton group

  • Miho AokiEmail author
  • Masanari Kida
Research
  • 19 Downloads

Abstract

In 1969, Laxton defined a multiplicative group structure on the set of rational sequences satisfying a fixed linear recurrence of degree two. He also defined some natural subgroups of the group, and determined the structures of their quotient groups. Nothing has been known about the structure of Laxton’s whole group and its interpretation. In this paper, we redefine his group in a natural way and determine the structure of the whole group, which clarifies Laxton’s results on the quotient groups. This definition makes it possible to use the group to show various properties of such sequences.

Keywords

Laxton groups Linear recurrence sequences Quadratic fields 

Mathematics Subject Classification

11B37 11B39 11R11 

Notes

Author's contributions

Acknowledgements

The authors would like to thank the referee for useful suggestions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Interdisciplinary Faculty of Science and EngineeringShimane UniversityMatsueJapan
  2. 2.Department of Mathematics, Faculty of Science Division ITokyo University of ScienceTokyoJapan

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