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Computing the table of marks of a cyclic extension. (English) Zbl 1282.20015
Summary: The subgroup pattern of a finite group \(G\) is the table of marks of \(G\) together with a list of representatives of the conjugacy classes of subgroups of \(G\). In this article we present an algorithm for the computation of the subgroup pattern of a cyclic extension of \(G\) from the subgroup pattern of \(G\). Repeated application of this algorithm yields an algorithm for the computation of the table of marks of a solvable group \(G\), along a composition series of \(G\).

MSC:
20C40 Computational methods (representations of groups) (MSC2010)
19A22 Frobenius induction, Burnside and representation rings
20B40 Computational methods (permutation groups) (MSC2010)
20D30 Series and lattices of subgroups
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
Software:
GAP; TomLib
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References:
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