Let V be a vector space over a field F of characteristic p and let T be a regular subgroup of the affine group AGL(V). In the finite dimensional case we show that, if T is abelian or p>0, then T is unipotent. For T abelian, pushing forward some ideas used by Caranti, Dalla Volta, Sala, we show that the set {t-I|t\in T} is a subalgebra of End_F(F+V), which is nilpotent when V has finite dimension. This allows a rather systematic construction of abelian regular subgroups.

Tamburini Bellani, M. C., Some remarks on regular subgroups of the affine group, <<INTERNATIONAL JOURNAL OF GROUP THEORY>>, 2012; (01): 17-23 [http://hdl.handle.net/10807/2817]

Some remarks on regular subgroups of the affine group

Tamburini Bellani, Maria Clara
2012

Abstract

Let V be a vector space over a field F of characteristic p and let T be a regular subgroup of the affine group AGL(V). In the finite dimensional case we show that, if T is abelian or p>0, then T is unipotent. For T abelian, pushing forward some ideas used by Caranti, Dalla Volta, Sala, we show that the set {t-I|t\in T} is a subalgebra of End_F(F+V), which is nilpotent when V has finite dimension. This allows a rather systematic construction of abelian regular subgroups.
2012
Inglese
Tamburini Bellani, M. C., Some remarks on regular subgroups of the affine group, <<INTERNATIONAL JOURNAL OF GROUP THEORY>>, 2012; (01): 17-23 [http://hdl.handle.net/10807/2817]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/2817
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