Subgroup Embeddings in the Symmetric Group of Degree Nine

Authors: Mysovskikh V.I.¹; Skopin A.I.²

Source: Journal of Mathematical Sciences, Volume 112, Number 4, December 2002 , pp. 4398-4399(2)

Publisher: Springer

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Abstract:

This paper is devoted to the determination of embedding properties of all nonprimary subgroups of the symmetric group on nine letters and continues previous investigations of the authors. The above-mentioned subgroups were tested for the following properties: abnormality, pronormality, paranormality, their weak analogs, weak normality, and the subnormalizer condition. The technique of Burnside marks, as well as respective information on the table of marks of S_9 from the TOM library of the computer algebra package GAP (Groups, Algorithms and Programming), were used. The subgroups of prime-power orders were not considered, because many of the above-mentioned concepts coincide for such subgroups. The total number of subgroups considered turned out to be 432. Bibliography: 18 titles.

Language: English

Document Type: Research article

Affiliations: 1: St.Petersburg State University 2: St.Petersburg Department of the Steklov Mathematical Institute

Publication date: 2002-12-01