The inductive blockwise Alperin weight condition for PSU(4, 3) and PSU(6, 2). Issue 1 (17th January 2022)

• Record Type: Journal Article
• Authors: Du, Yucong
• Is Part Of: Communications in algebra. Volume 50:Issue 1(2022)
• Page Start: 54
• Page End: 72
• Publication Date: 2022-01-17
• Subjects: Alperin weight conjecture -- PSU(4, 3) -- PSU(6, 2) -- the inductive blockwise Alperin weight condition; 20C20 -- 20C33; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1950746
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: In this note, we prove the inductive blockwise Alperin weight condition for PSU ( 4, 3 ) by establishing an equivariant bijection between 2-irreducible Brauer characters and 2-weights of the 2 ′ -cover of PSU ( 4, 3 ) and for PSU ( 6, 2 ) by establishing an equivariant bijection between 3-irreducible Brauer characters and 3-weights of the 3 ′ -cover of PSU ( 6, 2 ) . Thus the inductive blockwise Alperin weight condition holds for the simple groups PSU ( n, q ) with n ≤ 7 for every prime dividing its order, since the other cases are treated.