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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computing the table of marks of a cyclic extension


Authors: L. Naughton and G. Pfeiffer
Journal: Math. Comp. 81 (2012), 2419-2438
MSC (2010): Primary 20B40; Secondary 19A22, 20D30, 20D08, 20D10
Published electronically: February 24, 2012
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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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Additional Information

L. Naughton
Affiliation: School of Mathematics, Statistics and Applied Mathematics, NUI, Galway
Email: liam.naughton@nuigalway.ie

G. Pfeiffer
Affiliation: School of Mathematics, Statistics and Applied Mathematics, NUI, Galway
Email: goetz.pfeiffer@nuigalway.ie

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02600-7
PII: S 0025-5718(2012)02600-7
Received by editor(s): May 20, 2011
Received by editor(s) in revised form: July 27, 2011
Published electronically: February 24, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.