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A Note on the δ-length of Maximal Subgroups in Finite Soluble Groups

✍ Scribed by A. Ballester-Bolinches; M. D. Pérez-Ramos

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
253 KB
Volume
166
Category
Article
ISSN
0025-584X

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✦ Synopsis

A formation is a class 3 of groups which is closed under homomorphic images and is such that each group G has a unique smallest normal subgroup H with factor group in 5.

This uniquely determined normal subgroup of G is called the 8-residual subgroup of G and will be denoted here by G,. The formation 8 is said to be saturated if the group G belongs to 8 whenever the Frattini factor group G/@(G) is in 5.

The n-th term F,(G) of the Fitting series of a group G is defined inductively by F,(G) = 1 and F,, ,(G)/F,(G) = F(G/F,(C)), the Fitting subgroup of G/F,(G).

There exists an smallest n such that F,(G) = G. This number n is called the nilpotent length of G and it is denoted Let 8 be a saturated formation. We define the %-length of a group G as the nilpotent

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