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GROUPS SATISFYING THE DOUBLE CHAIN CONDITION ON ABELIAN SUBGROUPS

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  12 September 2018

MATTIA BRESCIA  and
ALESSIO RUSSO Open the ORCID record for ALESSIO RUSSO [Opens in a new window]
MATTIA BRESCIA
Affiliation:
Dipartimento di Matematica e Fisica, Università della Campania ‘Luigi Vanvitelli’, Viale Lincoln 5, Caserta, Italy email mattia.brescia@unicampania.it
ALESSIO RUSSO*
Affiliation:
Dipartimento di Matematica e Fisica, Università della Campania ‘Luigi Vanvitelli’, Viale Lincoln 5, Caserta, Italy email alessio.russo@unicampania.it
*
✉alessio.russo@unicampania.it
Rights & Permissions [Opens in a new window]

Abstract

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If $\unicode[STIX]{x1D703}$ is a subgroup property, a group $G$ is said to satisfy the double chain condition on $\unicode[STIX]{x1D703}$-subgroups if it admits no infinite double sequences

$$\begin{eqnarray}\cdots <X_{-n}<\cdots <X_{-1}<X_{0}<X_{1}<\cdots <X_{n}<\cdots\end{eqnarray}$$
consisting of $\unicode[STIX]{x1D703}$-subgroups. We describe the structure of generalised radical groups satisfying the double chain condition on abelian subgroups.

Keywords

double chain conditionabelian subgroup

MSC classification

Primary: 20E15: Chains and lattices of subgroups, subnormal subgroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 212 - 218
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The authors are members of GNSAGA-INdAM and this work was carried out within the ADV-AGTA project.

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