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PROFINITE GROUPS WITH FINITE VIRTUAL LENGTH

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  18 July 2013

NORBERTO GAVIOLI ,
VALERIO MONTI  and
CARLO MARIA SCOPPOLA
NORBERTO GAVIOLI
Affiliation:
Dipartimento di Ingegneria e, Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, via Vetoio, 1, I-67010 Coppito (L’Aquila) AQ, Italy email gavioli@univaq.it
VALERIO MONTI
Affiliation:
Dipartimento di Scienza, e Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio, 11, I-22100 Como, Italy email valerio.monti@uninsubria.it
CARLO MARIA SCOPPOLA*
Affiliation:
Dipartimento di Ingegneria e, Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, via Vetoio, 1, I-67010 Coppito (L’Aquila) AQ, Italy email gavioli@univaq.it
*
✉scoppola@univaq.it
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Abstract

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In this paper we introduce the notion of finite virtual length for profinite groups (that is, every series has a bounded number of infinite factors) and we prove a Jordan–Hölder type theorem for profinite groups with finite virtual length. More structural results are provided in the pronilpotent and $p$-adic analytic cases.

Keywords

profinite groups with operatorsJordan–Hölder theorempro-p groups

MSC classification

Secondary: 20E18: Limits, profinite groups 20E15: Chains and lattices of subgroups, subnormal subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 3 , December 2013 , pp. 343 - 355
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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