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44 lines
1.8 KiB
44 lines
1.8 KiB
<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE pkgmetadata SYSTEM "https://www.gentoo.org/dtd/metadata.dtd">
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<pkgmetadata>
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<maintainer type="person">
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<email>mjo@gentoo.org</email>
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</maintainer>
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<maintainer type="person">
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<email>frp.bissey@gmail.com</email>
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<name>François Bissey</name>
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</maintainer>
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<maintainer type="project" proxied="proxy">
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<email>proxy-maint@gentoo.org</email>
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<name>Proxy Maintainers</name>
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</maintainer>
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<maintainer type="project">
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<email>sci-mathematics@gentoo.org</email>
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<name>Gentoo Mathematics Project</name>
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</maintainer>
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<longdescription lang="en">
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The concept of a table of marks was introduced by W. Burnside in his
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1955 book Theory of Groups of Finite Order. Therefore a table of
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marks is sometimes called a Burnside matrix.
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The table of marks of a finite group G is a matrix whose rows and
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columns are labelled by the conjugacy classes of subgroups of G and
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where for two subgroups H and K the (H, K)-entry is the number of
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fixed points of K in the transitive action of G on the cosets of H
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in G. So the table of marks characterizes the set of all permutation
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representations of G. Moreover, the table of marks gives a compact
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description of the subgroup lattice of G, since from the numbers of
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fixed points the numbers of conjugates of a subgroup K contained in
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a subgroup H can be derived.
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For small groups the table of marks of G can be constructed directly
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in GAP by first computing the entire subgroup lattice of G. However,
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for larger groups this method is unfeasible. The GAP Table of Marks
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library provides access to several hundred tables of marks and their
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maximal subgroups.
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</longdescription>
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<upstream>
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<remote-id type="github">gap-packages/tomlib</remote-id>
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</upstream>
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</pkgmetadata>
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