Premium
An Alternating Sum Formula for Multiplicities of Lower Defect Groups
Author(s) -
Symonds Peter
Publication year - 1993
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/blms/25.2.121
Subject(s) - citation , mathematics , library science , combinatorics , computer science
Let G be a finite group and let k be an algebraically closed field of prime characteristic p. Let 5 b e a block of kG, P a /^-subgroup of G and n a /(-element of G. Then the multiplicity of P as a lower defect group of B for the /^-section of n is defined [1, 2, 4] and is denoted by mB(P). We shall prove the following induction theorem for mB(P) in terms of the Brown complex A of chains of non-trivial /^-subgroups of G.