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The Glauberman Correspondence and Subgroups of Operator Groups: a Counterexample
Author(s) -
Puin Christopher,
Wolf T. R.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002172
Subject(s) - counterexample , mathematics , automorphism , conjecture , mathematics subject classification , coprime integers , operator (biology) , combinatorics , pure mathematics , finite group , group (periodic table) , organic chemistry , transcription factor , gene , biochemistry , chemistry , repressor
Let G and A be finite groups with coprime orders, and suppose that A acts on G by automorphisms. Let π( G , A ):Irr A ( G )→Irr(C G ( A )) be the Glauberman–Isaacs correspondence. Let B ⩽ A and χ∈Irr A ( G ). We exhibit a counterexample to the conjecture that χπ( G , A ) is an irreducible constituent of the restriction of χπ( G , B ) to C G ( A ). 1991 Mathematics Subject Classification 20C15.