 
Summary: THE CONTROLLER SUBGROUP OF ONESIDED IDEALS IN
COMPLETED GROUP RINGS
KONSTANTIN ARDAKOV
Abstract. Let G be a compact padic analytic group and let I be a right
ideal of the Iwasawa algebra kG. A closed subgroup H of G is said to control
I if I can be generated as a right ideal by a subset of kH. We prove that the
intersection of any collection of such subgroups again controls I. This has an
application to the study of twosided ideals in nilpotent Iwasawa algebras.
1. Introduction
1.1. Controlling subgroups. Let G be a group and let k be a field. A subgroup
H of G is said to control a right ideal I of the group algebra k[G] if I can be
generated as a right ideal by a subset of the subalgebra k[H] of k[G], or equivalently,
if I = (I k[H]) · k[G]. It is clear that if I is controlled by a proper subgroup H
then I is completely determined by a right ideal in a smaller group algebra, namely
I k[H]. In the study of twosided ideals in group rings, theorems that assert
that under suitable conditions a twosided ideal is controlled by a known small
subgroup of the group are particularly desirable: a canonical example of such a
result is Zalesskii's Theorem [11], which asserts that every faithful prime ideal of
the group algebra of a finitely generated torsionfree nilpotent group is controlled
by the centre of the group.
