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AXIOMATISABILITY OF THE CLASS OF MONOLITHIC GROUPS IN A VARIETY OF NILPOTENT GROUPS

Part of: Varieties Representation theory of groups Structure and classification of infinite or finite groups Special aspects of infinite or finite groups Foundations

Published online by Cambridge University Press:  16 January 2020

JOSHUA T. GRICE Open the ORCID record for JOSHUA T. GRICE [Opens in a new window]
JOSHUA T. GRICE*
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC29208, USA email [email protected]
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Abstract

The class of all monolithic (that is, subdirectly irreducible) groups belonging to a variety generated by a finite nilpotent group can be axiomatised by a finite set of elementary sentences.

Keywords

subdirectly irreducible groupmonolithic groupnilpotent groupvariety of groupsfinite axiomatisability

MSC classification

Primary: 20A05: Axiomatics and elementary properties
Secondary: 08B10: Congruence modularity, congruence distributivity 20D15: Nilpotent groups, $p$-groups 20E10: Quasivarieties and varieties of groups 20F18: Nilpotent groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 67 - 76
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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References

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