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The number of blocks with a given defect group
Author(s) -
Barker Laurence
Publication year - 1997
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300012687
Subject(s) - mathematics , conjugacy class , combinatorics , rank (graph theory) , integer (computer science) , group (periodic table) , matrix (chemical analysis) , finite group , discrete mathematics , materials science , computer science , composite material , programming language , chemistry , organic chemistry
Given a p ‐subgroup P of a finite group G we express the number of p ‐blocks of G with defect group P as the p ‐rank of a symmetric integer matrix indexed by the N ( P )/ P ‐conjugacy classes in PC ( P )/ P . We obtain a combinatorial criterion for P to be a defect group in G .