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ON REGULAR SUBGROUPS OF THE AFFINE GROUP

Published online by Cambridge University Press:  08 October 2014

FRANCESCO CATINO
Affiliation:
Dipartimento di Matematica e Fisica ‘Ennio De Giorgi’, Università del Salento, Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy email francesco.catino@unisalento.it
ILARIA COLAZZO
Affiliation:
Dipartimento di Matematica e Fisica ‘Ennio De Giorgi’, Università del Salento, Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy email ilaria.colazzo@unisalento.it
PAOLA STEFANELLI
Affiliation:
Dipartimento di Matematica e Fisica ‘Ennio De Giorgi’, Università del Salento, Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy email paola.stefanelli@unisalento.it
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Abstract

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].

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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ON REGULAR SUBGROUPS OF THE AFFINE GROUP
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