On a modification of the group of circular units of a real abelian field

For a real abelian field K  , Sinnottʼs group of circular units CKCK is a subgroup of finite index in the full group of units EKEK playing an important role in Iwasawa theory. Let K∞/KK∞/K be the cyclotomic ZpZp-extension of K  , and hKnhKn be the class number of KnKn, the n  -th layer in K∞/KK∞/K. Then for p≠2p≠2 and n going to infinity, the p  -parts of the quotients [EKn:CKn]/hKn[EKn:CKn]/hKn stabilize. Unfortunately this is not the case for p=2p=2, when the group C1,KC1,K of all units of K  , whose squares belong to CKCK, is usually used instead of CKCK. But C1,KC1,K is better only for index formula purposes, not having the other nice properties of CKCK. The main aim of this paper is to offer another alternative to CKCK which can be used in cyclotomic ZpZp-extensions even for p=2p=2 still keeping almost all nice properties of CKCK.