Vol. 45, No. 2, 1973

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ISSN: 0030-8730
On generalizations of Sylow tower groups

Abi (Abiadbollah) Fattahi

Vol. 45 (1973), No. 2, 453–478
Abstract

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
Milestones
Received: 4 October 1971
Published: 1 April 1973
Authors
Abi (Abiadbollah) Fattahi