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SUBPERMUTABLE SUBGROUPS OF SKEW LINEAR GROUPS AND UNIT GROUPS OF REAL GROUP ALGEBRAS
Le, Qui Danh,Nguyen, Trung Nghia,Nguyen, Kim Ngoc Korean Mathematical Society 2021 대한수학회보 Vol.58 No.1
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)∗.