TY - JOUR

T1 - Fake Galois actions

AU - Farrell, Niamh

AU - Ruhstorfer, Lucas

N1 - Funding Information: The first author gratefully acknowledges financial support received from a London Mathematical Society 150th Anniversary Postdoctoral Mobility Grant, and from the DFG Project SFB-TRR 195. Funding Information: This paper is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the second author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2018 semester. The second author’s research was conducted in the framework of the research training group GRK 2240: Algebro-geometric Methods in Algebra, Arithmetic and Topology, which is funded by the DFG.

PY - 2020/8/20

Y1 - 2020/8/20

N2 - We prove that for all non-Abelian finite simple groups S, there exists a fake mth Galois action on IBr(X) with respect to X a- X a Š Aut(X), where X is the universal covering group of S and m is any non-negative integer coprime to the order of X. This is one of the two inductive conditions needed to prove an "-modular analogue of the Glauberman-Isaacs correspondence.

AB - We prove that for all non-Abelian finite simple groups S, there exists a fake mth Galois action on IBr(X) with respect to X a- X a Š Aut(X), where X is the universal covering group of S and m is any non-negative integer coprime to the order of X. This is one of the two inductive conditions needed to prove an "-modular analogue of the Glauberman-Isaacs correspondence.

KW - Brauer characters

KW - Clifford theory

KW - fake Galois actions

KW - finite reductive groups

KW - Modular Glauberman-Isaacs correspondence

UR - http://www.scopus.com/inward/record.url?scp=85095460172&partnerID=8YFLogxK

U2 - 10.1142/s0219498821501334

DO - 10.1142/s0219498821501334

M3 - Article

AN - SCOPUS:85095460172

VL - 20

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

SN - 0219-4988

IS - 8

M1 - 2150133

ER -