𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Top of the Lattice of Normal Subgroups of the Grigorchuk Group

✍ Scribed by Tullio Ceccherini-Silberstein; Fabio Scarabotti; Filippo Tolli

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
182 KB
Volume
246
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

A complete description of the lattice of all normal subgroups not contained in the stabilizer of the fourth level of the tree and, consequently, of index ≀ 2 12 in the Grigorchuk group G is given. This leads to the following sharp version of the congruence property: a normal subgroup not contained in the stabilizer at level n + 1 contains the stabilizer at level n + 3 (in fact such a normal subgroup contains the subgroup N n+1 ), but, in general, it does not contain the stabilizer at level n + 2. The determination of all normal subgroups at each level n β‰₯ 4 is then reduced to the analysis of certain G-modules which depend only on n and the previous description, as for the analogous problem for the automorphism group of the regular rooted tree.

πŸ“œ SIMILAR VOLUMES

On the MΓΆbius Number of the Subgroup Lat
On the MΓΆbius Number of the Subgroup Lattice of the Symmetric Group
✍ John Shareshian πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 460 KB

In this paper, a formula is given for the Mo bius number +(1, S n ) of the subgroup lattice of the symmetric group S n . This formula involves the Mo bius numbers of certain transitive subgroups of S n . When n has at most two (not necessarily distinct) prime factors or n is a power of two, this for

Subgroups of the Nottingham Group
Subgroups of the Nottingham Group
✍ Rachel Camina πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 214 KB
Normalizers of the Congruence Subgroups
Normalizers of the Congruence Subgroups of the Hecke Groups G4 and G6
✍ Mong-Lung Lang πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 137 KB

Normalizers of 1 0 (m)+w 2 and 1 0 (m)+w 3 in PSL 2 (R) are determined. The determination of such normalizers enables us to determine the normalizers (in PSL 2 (R)) of the congruence subgroups G 0 4 (A) and G 0 6 (A) of the Hecke groups G 4 and G 6 .