Vol. 45, No. 2, 1973

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On generalizations of Sylow tower groups

Abi (Abiadbollah) Fattahi

Vol. 45 (1973), No. 2, 453–478

In this paper two different generalizations of Sylow tower groups are studied. In Chapter I the notion of a k-tower group is introduced and a bound on the nilpotence length (Fitting height) of an arbitrary finite solvable group is found. In the same chapter a different proof to a theorem of Baer is given; and the list of all minimal-not-Sylow tower groups is obtained.

Further results are obtained on a different generalization of Sylow tower groups, called Generalized Sylow Tower Groups (GSTG) by J. Derr. It is shown that the class of all GSTG’s of a fixed complexion form a saturated formation, and a structure theorem for all such groups is given.

Mathematical Subject Classification 2000
Primary: 20D30
Received: 4 October 1971
Published: 1 April 1973
Abi (Abiadbollah) Fattahi