Infinite locally finite simple groups with many complemented subgroups

Document Type : Research Paper

Authors

1 Dipartimento di Matematica e Fisica, Universit degli Studi della Campania “Luigi Vanvitelli”, viale Lincoln 5, Caserta, Italy

2 Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Universit degli Studi di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, Napoli, Italy

Abstract

We prove that the following families of (infinite) groups have complemented subgroup lattice‎: ‎alternating groups‎, ‎finitary symmetric groups‎, ‎Suzuki groups over an infinite locally finite field of characteristic $2$‎, ‎Ree groups over an infinite locally finite field of characteristic~$3$‎. ‎We also show that if the Sylow primary subgroups of a locally finite simple group $G$ have complemented subgroup lattice‎, ‎then this is also the case for $G$‎.

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References

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International Journal of Group Theory
Volume 11, Issue 3 - Serial Number 3
September 2022
Pages 191-200

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History

  • Receive Date: 12 July 2021
  • Revise Date: 24 September 2021
  • Accept Date: 24 September 2021
  • Published Online: 01 September 2022

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