Colin D. Reid

Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups

We use the structure lattice, introduced in Part I, to undertake a systematic study of the class

Locally normal subgroups of totally disconnected groups. Part I: General theory

\mathscr S

The essentially chief series of a compactly generated locally compact group

consisting of compactly generated, topologically simple, totally disconnected locally compact groups that are non-discrete. Given

Locally normal subgroups of simple locally compact groups

G \in \mathscr S

On the structure of just infinite profinite groups

, we show that compact open subgroups of

Endomorphisms of profinite groups

G

The Generalised Pro-Fitting Subgroup of a Profinite Group

involve finitely many isomorphism types of composition factors, and do not have any soluble normal subgroup other than the trivial one. By results of Part I, this implies that the centraliser lattice and local decomposition lattice of

Subgroups of finite index and the just infinite property

G

Normal Subgroup Structure of Totally Disconnected Locally Compact Groups

are Boolean algebras. We show that the

THE NUMBER OF PROFINITE GROUPS WITH A SPECIFIED SYLOW SUBGROUP

G