On Clifford theory with Galois action

JOURNAL OF ALGEBRA

卷:457

Article

Ladisch, Frieder¹ 

[1] Univ Rostock, Inst Math, Ulmenstr 69,Haus 8, D-18057 Rostock, Germany

关键词: Brauer-Clifford group;    Clifford theory;    Character theory of finite groups;    Galois theory;    Schur indices;   

DOI  :  10.1016/j.jalgebra.2016.03.008

来源: Elsevier

【 摘 要 】

Let (G) over cap a be a finite group, N a normal subgroup of (G) over cap and v is an element of Irr N. Let F be a subfield of the complex numbers and assume that the Galois orbit of v over F is invariant in (G) over cap. We show that there is another triple ((G) over cap (1), N-1, v(1)) of the same form, such that the character theories of (G) over cap over v and of (G) over cap over v(1) are essentially the same over the field F and such that the following holds: (G) over cap (1) has a cyclic normal subgroup C contained in N-1, such that v(1) = lambda(N1) for some linear character lambda of C, and such that N-1/C is isomorphic to the (abelian) Galois group of the field extension F(lambda)/F(v(1)). More precisely, having the same character theory means that both triples yield the same element of the Brauer-Clifford group BrCliff(G,F(v)) defined by A. Turull. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free