The GAP Table of Marks Library TomLib. The concept of the table of marks of a finite group was first introduced by William Burnside in his famous book ”Theory of Groups of Finite order.” In fact many books refer to a table of marks as 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 A and B the (A,B) entry is the number of fixed points of B in the transitive action of G on the cosets of A 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 B contained in a subgroup A can be derived.
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References in zbMATH (referenced in 3 articles )
Showing results 1 to 3 of 3.
- Cannon, John; Garonzi, Martino; Levy, Dan; Maróti, Attila; Simion, Iulian I.: Groups equal to a product of three conjugate subgroups (2016)
- Menezes, Nina E.; Quick, Martyn; Roney-Dougal, Colva M.: The probability of generating a finite simple group. (2013)
- Naughton, L.; Pfeiffer, G.: Computing the table of marks of a cyclic extension. (2012)