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LOCALLY FINITE GROUPS WHOSE SUBGROUPS HAVE FINITE NORMAL OSCILLATION

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  20 November 2013

F. DE GIOVANNI ,
M. MARTUSCIELLO  and
C. RAINONE
F. DE GIOVANNI*
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I - 80126, Napoli, Italy
M. MARTUSCIELLO
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I - 80126, Napoli, Italy email maria.martusciello@unina.it
C. RAINONE
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I - 80126, Napoli, Italy email caterina.rainone@unina.it
*
✉degiovan@unina.it
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Abstract

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If $X$ is a subgroup of a group $G$, the cardinal number $\min \{ \vert X: X_{G}\vert , \vert {X}^{G} : X\vert \} $ is called the normal oscillation of $X$ in $G$. It is proved that if all subgroups of a locally finite group $G$ have finite normal oscillation, then $G$ contains a nilpotent subgroup of finite index.

Keywords

locally finite groupnormal oscillation

MSC classification

Secondary: 20F24: FC-groups and their generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 3 , June 2014 , pp. 479 - 487
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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