Given a regular subgroup R of AGLn(F), one can ask if R contains nontrivial translations. A negative answer to this question was given by Liebeck, Praeger and Saxl for AGL2(p) (p a prime), AGL3(p) (p odd) and for AGL4(2). A positive answer was given by Hegedűs for AGLn(p) when n≥4 if p is odd and for n=3 or n≥5 if p=2. A first generalization to finite fields of Hegedűs’ construction was recently obtained by Catino, Colazzo and Stefanelli. In this paper we give examples of such subgroups in AGLn(F) for any n≥5 and any field F. For n<5 we provide necessary and sufficient conditions for their existence, assuming R to be unipotent if charF=0

Pellegrini, M. A., Tamburini Bellani, M. C., Regular subgroups of the affine group with no translations, <<JOURNAL OF ALGEBRA>>, 2017; 478 (15 May 2017): 410-418. [doi:10.1016/j.jalgebra.2017.01.045] [http://hdl.handle.net/10807/96869]

Regular subgroups of the affine group with no translations

Pellegrini, Marco Antonio
Primo
;
Tamburini Bellani, Maria Clara
Ultimo
2017

Abstract

Given a regular subgroup R of AGLn(F), one can ask if R contains nontrivial translations. A negative answer to this question was given by Liebeck, Praeger and Saxl for AGL2(p) (p a prime), AGL3(p) (p odd) and for AGL4(2). A positive answer was given by Hegedűs for AGLn(p) when n≥4 if p is odd and for n=3 or n≥5 if p=2. A first generalization to finite fields of Hegedűs’ construction was recently obtained by Catino, Colazzo and Stefanelli. In this paper we give examples of such subgroups in AGLn(F) for any n≥5 and any field F. For n<5 we provide necessary and sufficient conditions for their existence, assuming R to be unipotent if charF=0
Inglese
Pellegrini, M. A., Tamburini Bellani, M. C., Regular subgroups of the affine group with no translations, <<JOURNAL OF ALGEBRA>>, 2017; 478 (15 May 2017): 410-418. [doi:10.1016/j.jalgebra.2017.01.045] [http://hdl.handle.net/10807/96869]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/96869
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