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Why is space three-dimensional and how may groups be seen?

Abstract

First we propose a model of visual perception essentially based on the Keldysh-Chernavsky-Sossinsky ‘three-channel theorem’, from which three-dimensionality of space follows. Second, we associate with a system of subgroups H 1, ..., Hs of a given group G a geometric object, called a group crystal, in order to visualize G. How this notion works is illustrated via the Burnside problem.

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References

  1. SossinskyA. B.: ‘Tolerance Space Theory and Some Application’, Acta Appl. Math. 5 (1986), 137–167 (this issue).

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  2. Adjan, S. I.: ‘The Burnside Problem and Identities in Groups’, Nauka, Moscow, 1975 (English translation: the Springer “Ergebnisse” series, 1979).

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Vinogradov, A.M. Why is space three-dimensional and how may groups be seen?. Acta Appl Math 5, 169–180 (1986). https://doi.org/10.1007/BF00046586

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  • DOI: https://doi.org/10.1007/BF00046586

AMS (MOS) subject classifications (1980)

  • 94A99
  • 92A27
  • 20F32
  • 20C99

Key words

  • Tolerance space
  • visual perception
  • group crystal
  • Burnside problem