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AUTOMORPHISM CRITERIA FOR M*-GROUPS

Published online by Cambridge University Press:  01 July 2004

Emilio Bujalance ,
Francisco-Javier Cirre  and
Peter Turbek
Emilio Bujalance
Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Madrid 28040, Spain (eb@mat.uned.es; jcirre@mat.uned.es)
Francisco-Javier Cirre
Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Madrid 28040, Spain (eb@mat.uned.es; jcirre@mat.uned.es)
Peter Turbek
Affiliation:
Department of Mathematics, Computer Science and Statistics, Purdue University Calumet, Hammond, IN 46323, USA (turbek@nwi.calumet.purdue.edu)
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Abstract

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We prove that the determination of all $M^*$-groups is essentially equivalent to the determination of finite groups generated by an element of order 3 and an element of order 2 or 3 that admit a particular automorphism. We also show how the second commutator subgroup of an $M^*$-group $G$ can often be used to construct $M^*$-groups which are direct products with $G$ as one factor. Several applications of both methods are given.

AMS 2000 Mathematics subject classification: Primary 20D45; 20E36. Secondary 14H37; 30F50

Keywords

M*-groupsautomorphisms of groupsKlein surfacesreal algebraic curves
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 2 , June 2004 , pp. 339 - 351
Copyright
Copyright © Edinburgh Mathematical Society 2004