On the structure of virtually nilpotent compact p-adic analytic groups

@article{Woods2016OnTS,
title={On the structure of virtually nilpotent compact p-adic analytic groups},
author={William Woods},
journal={Journal of Group Theory},
year={2016},
volume={21},
pages={165 - 188}
}
• William Woods
• Published 10 August 2016
• Mathematics
• Journal of Group Theory
Abstract Let G be a compact p-adic analytic group. We recall the well-understood finite radical Δ + {\Delta^{+}} and FC-centre Δ, and introduce a p-adic analogue of Roseblade’s subgroup nio ⁢ ( G ) {\mathrm{nio}(G)} , the unique largest orbitally sound open normal subgroup of G. Further, when G is nilpotent-by-finite, we introduce the finite-by-(nilpotent p-valuable) radical 𝐅𝐍 p ⁢ ( G ) {\mathbf{FN}_{p}(G)} , an open characteristic subgroup of G contained in nio ⁢ ( G ) {\mathrm{nio}(G…
6 Citations
Maximal prime homomorphic images of mod-p Iwasawa algebras
• William Woods
• Mathematics
Mathematical Proceedings of the Cambridge Philosophical Society
• 2016
Let k be a finite field of characteristic p, and G a compact p-adic analytic group. Write kG for the completed group ring of G over k. In this paper, we describe the structure of the ring kG/P, where
Extensions of almost faithful prime ideals in virtually nilpotent mod-p Iwasawa algebras
Let $G$ be a nilpotent-by-finite compact $p$-adic analytic group for some $p>2$, and $H = \mathbf{FN}_p(G)$ its finite-by-(nilpotent $p$-valuable) radical. Fix a finite field $k$ of characteristic
On the catenarity of virtually nilpotent mod-p Iwasawa algebras
Let $p>2$ be a prime, $k$ a finite field of characteristic $p$, and $G$ a nilpotent-by-finite compact $p$-adic analytic group. Write $kG$ for the completed group ring of $G$ over $k$. We show that
Dimension Theory in Iterated Local Skew Power Series Rings
• Billy Woods
• Mathematics
Algebras and Representation Theory
• 2022
Many well-known local rings, including soluble Iwasawa algebras and certain completed quantum algebras, arise naturally as iterated skew power series rings. We calculate their Krull and global

References

SHOWING 1-10 OF 15 REFERENCES
LOCALISATION AT AUGMENTATION IDEALS IN IWASAWA ALGEBRAS
• K. Ardakov
• Mathematics
Glasgow Mathematical Journal
• 2006
Let $G$ be a compact $p$-adic analytic group and let $\Lambda_G$ be its completed group algebra with coefficient ring the $p$-adic integers $\mathbb{Z}_p$. We show that the augmentation ideal in
Prime ideals in nilpotent Iwasawa algebras
Let G be a nilpotent complete p-valued group of finite rank and let k be a field of characteristic p. We prove that every faithful prime ideal of the Iwasawa algebra kG is controlled by the centre of
Primeness, semiprimeness and localisation in Iwasawa algebras
• Mathematics
• 2004
Necessary and sufficient conditions are given for the completed group algebras of a compact p-adic analytic group with coefficient ring the p-adic integers or the field of p elements to be prime,
The algebraic structure of group rings
$m_{i}$ . Then $A_{i}$ has the rank $r_{i}q_{i}^{2}m_{i}^{2}$ over K. We shall call the numbers $n\ell_{i}$ the Sckur indice $s^{\neg}$ of $\mathfrak{G}$ , since they first occurred in the work of 1.
Analytic Pro-P Groups
• Mathematics
• 1999
Prelude Part I. Pro-p Groups: 1. Profinite groups and pro-p groups 2. Powerful p-groups 3. Pro-p groups of finite rank 4. Uniformly powerful groups 5. Automorphism groups Interlude A. Fascicule de
Noncommutative Noetherian Rings
• Mathematics
• 2001
Articles on the history of mathematics can be written from many dierent perspectives. Some aim to survey a more or less wide landscape, and require the observer to watch from afar as theories develop
POLYCYCLIC-BY-FINITE GROUP ALGEBRAS ARE CATENARY
• Mathematics
• 1998
We show that group algebras kG of polycyclic-by-finite groups G, where k is a field, are catenary: If P = I0 ( I1 ( � � � ( Im = Pand P = J0 ( J2 ( � � � ( Jn = Pare both saturated chains of prime
A Course in the Theory of Groups
This is a detailed introduction to the theory of groups: finite and infinite; commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the