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Investigation of Subgroup Embeddings by the Computer Algebra Package GAP

In: Computer Algebra in Scientific Computing CASC’99

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  • V. I. Mysovskikh

    (St.Petersburg State University, Dept. of Math. and Mechanics St.Petersburg)

Abstract

We describe algorithms for testing subgroups of a finite group for subgroup embedding properties. The latter include abnormality, pronormality, para-normality, their weak analogies, the subnormalizer condition and weak normality (in the sense of K.H.Müller). The algorithms are based on the usage of tables of marks (Burnside matrices). This tool allows us to carry out calculations with integers instead of computations with group elements. Our implementation within the computer algebra package GAP is also considered. The respective codes are written in the GAP language. Two long-standing problems in the area were solved with the help of these programs. The respective counterexamples are described.

Suggested Citation

  • V. I. Mysovskikh, 1999. "Investigation of Subgroup Embeddings by the Computer Algebra Package GAP," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC’99, pages 309-315, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-60218-4_24
    DOI: 10.1007/978-3-642-60218-4_24
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