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ON REGULAR SUBGROUPS OF THE AFFINE GROUP

Part of: Radicals and radical properties of rings Permutation groups

Published online by Cambridge University Press:  08 October 2014

FRANCESCO CATINO ,
ILARIA COLAZZO  and
PAOLA STEFANELLI
FRANCESCO CATINO*
Affiliation:
Dipartimento di Matematica e Fisica ‘Ennio De Giorgi’, Università del Salento, Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy email [email protected]
ILARIA COLAZZO
Affiliation:
Dipartimento di Matematica e Fisica ‘Ennio De Giorgi’, Università del Salento, Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy email [email protected]
PAOLA STEFANELLI
Affiliation:
Dipartimento di Matematica e Fisica ‘Ennio De Giorgi’, Università del Salento, Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy email [email protected]
*
✉[email protected]
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Abstract

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Catino and Rizzo [‘Regular subgroups of the affine group and radical circle algebras’, Bull. Aust. Math. Soc.79 (2009), 103–107] established a link between regular subgroups of the affine group and the radical brace over a field on the underlying vector space. We propose new constructions of radical braces that allow us to obtain systematic constructions of regular subgroups of the affine group. In particular, this approach allows to put in a more general context the regular subgroups constructed in Tamburini Bellani [‘Some remarks on regular subgroups of the affine group’ Int. J. Group Theory, 1 (2012), 17–23].

Keywords

affine groupregular subgroupbrace

MSC classification

Primary: 20B10: Characterization theorems
Secondary: 16N20: Jacobson radical, quasimultiplication
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 76 - 85
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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