On the Deskins completions, theta completions and theta pairs for maximal subgroups. II. (English) Zbl 0911.20018

Author’s abstract: This paper is a continuation of the paper reviewed above [see Zbl 0911.20017]. There we introduced the concept of \(\theta\)-completions associated with a maximal subgroup of a finite group. The concept offers a convenience for us to study the completions introduced by Deskins and gives us a way to reveal the relationship between the concepts of completions and \(\theta\)-pairs, the latter concept introduced by Mukherjee and Bhattacharya. The present paper is devoted to discussing the \(\pi\)-solvability, \(\pi\)-supersolvability and \(\pi\)-nilpotency of a finite group by using the \(\theta\)-completions. Moreover, a new proof on the Deskins conjecture concerning the supersolvability is included.


20D25 Special subgroups (Frattini, Fitting, etc.)
20E28 Maximal subgroups
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure


Zbl 0911.20017
Full Text: DOI


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[10] DOI: 10.1080/00927879808826142 · Zbl 0895.16019
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