Archive for Mathematical Logic 33 (1):23-34 (1994)

The following theorems are proved about the Frattini-free componentG Φ of a soluble stable ℜ-group: a) If it has a normal subgroupN with nilpotent quotientG Φ/N, then there is a nilpotent subgroupH ofG Φ withG Φ=NH. b) It has Carter subgroups; if the group is small, they are all conjugate. c) Nilpotency modulo a suitable Frattini-subgroup (to be defined) implies nilpotency. The last result makes use of a new structure theorem for the centre of the derivative of the Frattini-free component of a centreless soluble ℜ-group
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DOI 10.1007/BF01275468
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References found in this work BETA

Small Stable Groups and Generics.Frank O. Wagner - 1991 - Journal of Symbolic Logic 56 (3):1026-1037.
More on ${\germ R}$.Frank O. Wagner - 1992 - Notre Dame Journal of Formal Logic 33 (2):159-174.
Stable Groups, Mostly of Finite Exponent.Frank O. Wagner - 1993 - Notre Dame Journal of Formal Logic 34 (2):183-192.

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Conjugacy of Carter Subgroups in Groups of Finite Morley Rank.Olivier Frécon - 2008 - Journal of Mathematical Logic 8 (1):41-92.

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