gap-table-of-marks 1r2p6-1 / usr / share / doc-base / gap-tomlib

Document: gap-tomlib
Title: The GAP Library of Tables of Marks
Author: Liam Naughton, Götz Pfeiffer
Abstract:
 The  concept  of  a  Table of Marks was introduced by W.Burnside in his book
 "Theory  of Groups of Finite Order". Therefore a table of marks is
 sometimes  called  a Burnside matrix. The table of marks of a finite group G
 is  a matrix whose rows and columns are labelled by the conjugacy classes of
 subgroups  of  G and where for two subgroups H and K the (H, K)-entry is the
 number of fixed points of K in the transitive action of G on the cosets of H
 in  G.  So  the  table  of  marks  characterizes  the set of all permutation
 representations  of  G.  Moreover,  the  table  of  marks  gives  a  compact
 description  of  the  subgroup lattice of G, since from the numbers of fixed
 points  the  numbers of conjugates of a subgroup K contained in a subgroup H
 can  be derived. For small groups the table of marks of G can be constructed
 directly  in  GAP  by  first  computing  the  entire  subgroup lattice of G.
 However, for larger groups this method is unfeasible. The GAP Table of Marks
 library  provides access to several hundred table of marks and their maximal
 subgroups.
Section: Science/Mathematics

Format: pdf
Files: /usr/share/gap/pkg/tomlib/doc/manual.pdf

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Index: /usr/share/gap/pkg/tomlib/doc/chap0.html
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