Investigation of Subgroup Embeddings by the Computer Algebra Package GAP

V. I. Mysovskikh ()
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V. I. Mysovskikh: St.Petersburg State University, Dept. of Math. and Mechanics St.Petersburg

A chapter in Computer Algebra in Scientific Computing CASC’99, 1999, pp 309-315 from Springer

Abstract: 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.

Keywords: Normal Subgroup; Finite Group; Conjugacy Class; Proper Normal Subgroup; Respective Code (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-60218-4_24

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DOI: 10.1007/978-3-642-60218-4_24

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