Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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NOTES ON GENERALIZED POWER CENTRAL GROUP IDENTITIES IN SKEW GROUP ALGEBRAS

  • Nguyen Cao Dang (Faculty of Mathematics and Computer Science University of Science and Vietnam National University) ;
  • Le Qui Danh (University of Architecture Ho Chi Minh City)
  • Received : 2025.06.22
  • Accepted : 2026.04.10
  • Published : 2026.07.31
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Abstract

Let K𝜎G be the skew group algebra over a non-absolute field K of a locally finite group G induced by a group homomorphism 𝜎 : G → Aut(K). We investigate conditions under which the unit group 𝒰 (K𝜎G) satisfies a strict generalized power central group identity.

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Acknowledgement

The authors are grateful to Professor Mai Hoang Bien for his insightful discussions and valuable comments regarding this paper. The authors would also like to thank the referees for their careful reading of the manuscript and for their constructive comments, which have significantly improved the presentation of this paper. This research is funded by Vietnam National University of Ho Chi Minh City (VNU-HCM) under grant number T2025-18-02.