Some rank six geometries for the smallest Fischer sporadic simple group

Document Type : Full Length Article

Authors

1 Department of Computer Science, University of Garmsar, Address Garmsar, Semnan 3588115589, I. R. Iran

2 Faculty of Electrical & Computer Engineering, Malek Ashtar University of Technology, Tehran, I. R. Iran

Abstract

This paper introduces some new rank six geometries associated with the Fischer sporadic simple group Fi22. These geometries are both residually connected and firm, with Fi22 acts as a flag-transitive automorphism group on them. The previously known geometries for Fischer sporadic simple group Fi22 have rank at most four. Therefore, we investigate improvements to the lower bound of the maximum rank of the residually connected and firm geometries on which the group Fi22 acts as a flag-transitive automorphism group. Moreover, we demonstrate that the independent generating
set of Fischer sporadic simple group Fi22 has a size of at least seven.

Graphical Abstract

Some rank six geometries for the smallest Fischer sporadic simple group

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References

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Journal of Discrete Mathematics and Its Applications
Volume 10, Issue 1
March 2025
Pages 1-10

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History

  • Receive Date: 11 January 2025
  • Revise Date: 11 February 2025
  • Accept Date: 11 February 2025
  • First Publish Date: 01 March 2025
  • Publish Date: 01 March 2025

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