On finite minimal non-nilpotent groups
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- by A. Ballester-Bolinches, R. Esteban-Romero and Derek J. S. Robinson PDF
- Proc. Amer. Math. Soc. 133 (2005), 3455-3462 Request permission
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.References
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Additional Information
- A. Ballester-Bolinches
- Affiliation: Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, E-46100 Burjassot, València, Spain
- MR Author ID: 263725
- Email: Adolfo.Ballester@uv.es
- R. Esteban-Romero
- Affiliation: Departament de Matemàtica Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, E-46022 València, Spain
- MR Author ID: 689040
- ORCID: 0000-0002-2321-8139
- Email: resteban@mat.upv.es
- Derek J. S. Robinson
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
- Email: robinson@math.uiuc.edu
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 3455-3462
- MSC (2000): Primary 20D10
- DOI: https://doi.org/10.1090/S0002-9939-05-07996-7
- MathSciNet review: 2163579