Hausdorff dimension, pro-𝑝 groups, and Kac-Moody algebras
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Publication:4372615
DOI10.1090/S0002-9947-97-01918-1zbMath0892.20020MaRDI QIDQ4372615
Publication date: 16 December 1997
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Kac-Moody algebrasfiltrationspro-\(p\) groupsclosed subgroupsHausdorff dimensionsNottingham groupsanalytic profinite groupsdescending chains of normal subgroups
Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Compact groups (22C05) Hausdorff and packing measures (28A78) Limits, profinite groups (20E18) Associated Lie structures for groups (20F40)
Related Items (38)
Dimension and randomness in groups acting on rooted trees ⋮ New just-infinite pro-\(p\) groups of finite width and subgroups of the Nottingham group. ⋮ The smallest Mealy automaton of intermediate growth. ⋮ Unnamed Item ⋮ Every matrix is a product of Toeplitz matrices ⋮ The finitely generated Hausdorff spectra of a family of pro-\(p\) groups ⋮ The true prosoluble completion of a group: examples and open problems. ⋮ Hausdorff dimension in a family of self-similar groups. ⋮ Galois groups of tamely ramified \(p\)-extensions ⋮ A pro-2 group with full normal Hausdorff spectra ⋮ Strong approximation in random towers of graphs. ⋮ Congruence subgroup growth of arithmetic groups in positive characteristic. ⋮ Coverings and dimensions in infinite profinite groups ⋮ A pro‐pgroup with full normal Hausdorff spectra ⋮ Hausdorff dimensions in \(p\)-adic analytic groups ⋮ \(p\)-Basilica groups ⋮ Less than continuum many translates of a compact nullset may cover any infinite profinite group ⋮ Hausdorff dimension of some groups acting on the binary tree ⋮ On the Basilica operation ⋮ The equations satisfied by GGS-groups and the Abelian group structure of the Gupta-Sidki group. ⋮ Index-subgroups of the Nottingham group. ⋮ Pro‐p groups of positive rank gradient and Hausdorff dimension ⋮ GGS-groups: Order of congruence quotients and Hausdorff dimension ⋮ On the verbal width of finitely generated pro-\(p\) groups. ⋮ Branch rings, thinned rings, tree enveloping rings. ⋮ Hausdorff dimension in \(R\)-analytic profinite groups ⋮ Algebra, geometry, and topology of the substitution group of formal power series ⋮ The pro-\(p\) group of upper unitriangular matrices ⋮ FINITELY CONSTRAINED GROUPS OF MAXIMAL HAUSDORFF DIMENSION ⋮ On the commensurator of the Nottingham group ⋮ Standard Hausdorff spectrum of compact \(\mathbb{F}_pt\)-analytic groups ⋮ Hausdorff dimension of the second Grigorchuk group ⋮ The congruence subgroup problem for a family of branch groups ⋮ A pro-\(p\) group with infinite normal Hausdorff spectra ⋮ Spinal groups: semidirect product decompositions and Hausdorff dimension ⋮ Graded subalgebras of affine Kac-Moody algebras ⋮ Hereditarily just infinite profinite groups with complete Hausdorff dimension spectrum ⋮ On Subgroups of the Nottingham Group of Positive Hausdorff Dimension
Cites Work
- Powerful \(p\)-groups. II: \(p\)-adic analytic groups
- Graded subalgebras of affine Kac-Moody algebras
- On some \(\Lambda\)-analytic pro-\(p\) groups
- Subgroups of the Nottingham group
- On periodic compact groups
- \(p\)-adic analytic groups
- Growth Functions, p -Adic Analytic Groups, and Groups of Finite Coclass
- The maximal subgroups of the classical groups
- Semisimple subalgebras of semisimple Lie algebras
- Subgroups and subrings of profinite rings
- Introduction to Lie Algebras and Representation Theory
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