## 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.

### MSC:

 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:

### References:

 [1] DOI: 10.1016/0022-4049(90)90150-G · Zbl 0699.20016 [2] DOI: 10.1080/00927879608825807 · Zbl 0892.20021 [3] DOI: 10.1016/0022-4049(86)90074-5 · Zbl 0597.20014 [4] Deskins, W.E. On maximal subgroups. Proc. Sympos. Pure Math. Vol. 1, pp.100–104. Amer. Math. Soc. · Zbl 0096.24801 [5] DOI: 10.1007/BF01188517 · Zbl 0665.20008 [6] Huppert B., Endliche Gruppen I (1967) · Zbl 0217.07201 [7] DOI: 10.1090/S0002-9939-1990-1015683-9 [8] DOI: 10.1080/00927879608825821 · Zbl 0891.17020 [9] DOI: 10.1080/00927879508825331 · Zbl 0830.20045 [10] DOI: 10.1080/00927879808826142 · Zbl 0895.16019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.