Generalized Kaloujnine groups, uniseriality and height of automorphisms

被引：7

作者：

Ceccherini-Silberstein, TG

Leonov, YG

Scarabotti, F

Tolli, F

机构：

[1] Univ Sannio, Dipartimento Ingn, I-82100 Benevento, Italy

[2] Odessa Natl Acad Telecommun, Dept Comp Sci, UA-65000 Odessa, Ukraine

[3] Univ Roma La Sapienza, Dept MeMoMat, I-00161 Rome, Italy

[4] Univ Roma 3, Dipartimento Matemat, I-00146 Rome, Italy

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2005年 / 15卷 / 03期

关键词：

groups acting on trees; Lie action; uniseriality; Radon transform; characteristic subgroups;

D O I：

10.1142/S0218196705002372

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：503 / 527

页数：25