Computing the Table of Marks of a Cyclic Extension

2011/05/20 by Liam Naughton, Naughton, Liam, Goetz Pfeiffer +1
Mathematics · #20D08 #20D10 #20D30 #FOS: Mathematics #Group Theory (math.GR) #Primary 20B40 #Secondary 19A22 #math.GR #msc:19A22 #msc:20B40 #msc:20D08 #msc:20D10 #msc:20D30

paper · pdf · doi:10.48550/arxiv.1105.4064

20 pages

arxiv created 2011/05/20 · arxiv updated 2011/05/23

Abstract

The subgroup pattern of a finite groups 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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