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SUBPERMUTABLE SUBGROUPS OF SKEW LINEAR GROUPS AND UNIT GROUPS OF REAL GROUP ALGEBRAS

  • Le, Qui Danh (Department of Mathematics, Mechanics and Informatics University of Architecture Ho Chi Minh City) ;
  • Nguyen, Trung Nghia (Faculty of Mathematics and Computer Science University of Science) ;
  • Nguyen, Kim Ngoc (Faculty of Mathematics and Computer Science University of Science)
  • Received : 2020.03.06
  • Accepted : 2020.07.09
  • Published : 2021.01.31

Abstract

Let D be a division ring and n > 1 be an integer. In this paper, it is shown that if D ≠ ��3, then every subpermutable subgroup of the general skew linear group GLn(D) is normal. By applying this result, we show that every subpermutable subgroup of the unit group (ℝG)∗ of the real group algebras RG of finite groups G is normal in (ℝG)∗.

Keywords

References

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