Computing the table of marks of a cyclic extension

Naughton, L.; Pfeiffer, G.

doi:10.1090/S0025-5718-2012-02600-7

Computing the table of marks of a cyclic extension
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by L. Naughton and G. Pfeiffer PDF

Math. Comp. 81 (2012), 2419-2438 Request permission

Abstract:

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 $G$.

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