We show that the Lie action of the Kaloujnine group K(p, n) on the vector space (Fp)(pn) is uniserial. Using some Radon transform techniques we derive a formula for the height of the elements in K(p, n). A generalization of the Kaloujnine groups is introduced by considering automorphisms of a spherically homogeneous tree. We observe that uniseriality fails to hold for these groups and determine their lower central series; finally we discuss in detail Kaloujnine's description of the characteristic subgroups in terms of the (normal) "parallelotopic" subgroups.

Generalized Kaloujnine groups, uniseriality and height of automorphisms / Scarabotti, Fabio; Tullio G., Ceccherini Silberstein; Yurij G., Leonov; Filippo, Tolli. - In: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION. - ISSN 0218-1967. - STAMPA. - 15:3(2005), pp. 503-527. [10.1142/s0218196705002372]

Generalized Kaloujnine groups, uniseriality and height of automorphisms

SCARABOTTI, Fabio;
2005

Abstract

We show that the Lie action of the Kaloujnine group K(p, n) on the vector space (Fp)(pn) is uniserial. Using some Radon transform techniques we derive a formula for the height of the elements in K(p, n). A generalization of the Kaloujnine groups is introduced by considering automorphisms of a spherically homogeneous tree. We observe that uniseriality fails to hold for these groups and determine their lower central series; finally we discuss in detail Kaloujnine's description of the characteristic subgroups in terms of the (normal) "parallelotopic" subgroups.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/71457
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