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Finite groups in which some property of two-generator subgroups is transitive

Published online by Cambridge University Press:  17 April 2009

Costantino Delizia ,
Primoz Moravec  and
Chiara Nicotera
Costantino Delizia
Affiliation:
Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte don Melillo, 84084 - Fisciano (SA), Italy, e-mail: cdelizia@unisa.it
Primoz Moravec
Affiliation:
Dipartimento di Matematica e Informatica, Universita di Salerno, Via Ponte don Melillo, 84084 - Fisciano (SA), Italy, e-mail: cnicotera@unisa.it
Chiara Nicotera
Affiliation:
Fakulteta za Matematiko in Fiziko, Univerza v Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia, e-mail: primoz.moravec@fmf.uni-lj.si
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Finite groups in which a given property of two-generator subgroups is a transitive relation are investigated. We obtain a description of such groups and prove in particular that every finite soluble-transitive group is soluble. A classification of finite nilpotent-transitive groups is also obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 2 , April 2007 , pp. 313 - 320
Copyright
Copyright © Australian Mathematical Society 2007

References

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