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On partial ordering of chief factors in solvable groups

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Abstract

The isomorphism classes of chief factors in a finite solvable group are partially ordered by taking one class higher than the other if a member of the first class appears as a chief factor of the action of the group on a member of the second class. Together with this partial ordering the characteristics of the chief factors are considered. It is shown that the two conditions found by G. Pazderski are not only necessary but also sufficient for a partially ordered set and a function to be representable as the poset of isomorphism classes of chief factors in a finite solvable group with the chief factors having the prescribed characteristics. In addition, the construction yields that every finite distributive lattice is the lattice of normal subgroups of some finite solvable group.

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  1. Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13-15, 1364, Budapest, Hungary

    P. P. Pálfy

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  1. P. P. Pálfy
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Pálfy, P.P. On partial ordering of chief factors in solvable groups. Manuscripta Math 55, 219–232 (1986). https://doi.org/10.1007/BF01168687

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  • DOI: https://doi.org/10.1007/BF01168687

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