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Proceedings of the American Mathematical Society

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On finite minimal non-nilpotent groups

Authors: A. Ballester-Bolinches, R. Esteban-Romero and Derek J. S. Robinson
Journal: Proc. Amer. Math. Soc. 133 (2005), 3455-3462
MSC (2000): Primary 20D10
Published electronically: June 8, 2005
MathSciNet review: 2163579
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Abstract: A critical group for a class of groups $\mathfrak{X}$ is a minimal non- $\mathfrak{X}$-group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also called Schmidt groups) is given, together with a complete proof of Gol'fand's theorem on maximal Schmidt groups.

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Additional Information

A. Ballester-Bolinches
Affiliation: Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, E-46100 Burjassot, València, Spain

R. Esteban-Romero
Affiliation: Departament de Matemàtica Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, E-46022 València, Spain

Derek J. S. Robinson
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801

Received by editor(s): December 12, 2003
Received by editor(s) in revised form: July 16, 2004
Published electronically: June 8, 2005
Additional Notes: This work was supported by Proyecto BFM2001-1667-C03-03 (MCyT) and FEDER (European Union)
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2005 American Mathematical Society