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ON GROUPS WITH ALL SUBGROUPS SUBNORMAL OR SOLUBLE OF BOUNDED DERIVED LENGTH

Published online by Cambridge University Press:  13 August 2013

KIVANÇ ERSOY ,
ANTONIO TORTORA  and
MARIA TOTA
KIVANÇ ERSOY
Affiliation:
Department of Mathematics, Mimar Sinan Fine Arts Universityİstanbul 34427, Turkey e-mail: [email protected]
ANTONIO TORTORA
Affiliation:
Dipartimento di Matematica, Università di Salerno Via Giovanni Paolo II, 132 - Fisciano (SA) 84084, Italy e-mail: [email protected], [email protected]
MARIA TOTA
Affiliation:
Dipartimento di Matematica, Università di Salerno Via Giovanni Paolo II, 132 - Fisciano (SA) 84084, Italy e-mail: [email protected], [email protected]
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Abstract

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In this paper we deal with locally graded groups whose subgroups are either subnormal or soluble of bounded derived length, say d. In particular, we prove that every locally (soluble-by-finite) group with this property is either soluble or an extension of a soluble group of derived length at most d by a finite group, which fits between a minimal simple group and its automorphism group. We also classify all the finite non-abelian simple groups whose proper subgroups are metabelian.

Keywords

20F1920E32
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 1 , January 2014 , pp. 221 - 227
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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