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@article{1106916, author = {Bulant, Michal and Kučera, Radan}, article_number = {9}, doi = {http://dx.doi.org/10.1016/j.jnt.2013.03.009}, keywords = {Real abelian field; Zpextension; Group of circular units}, language = {eng}, issn = {0022314X}, journal = {Journal of Number Theory}, title = {On a modification of the group of circular units of a real abelian field}, volume = {133}, year = {2013} }
TY  JOUR ID  1106916 AU  Bulant, Michal  Kučera, Radan PY  2013 TI  On a modification of the group of circular units of a real abelian field JF  Journal of Number Theory VL  133 IS  9 SP  3138  3148 EP  3138  3148 PB  Elsevier SN  0022314X KW  Real abelian field KW  Zpextension KW  Group of circular units N2  For a real abelian field K, Sinnott's group of circular units C_K is a subgroup of finite index in the full group of units E_K playing an important role in Iwasawa theory. Let K_infty/K be the cyclotomic Z(p)extension of K, and h(Kn) be the class number of K_n, the nth layer in K_infty/K. Then for p<>2 and n going to infinity, the pparts of the quotients [E_Kn : C_Kn]/h(Kn) stabilize. Unfortunately this is not the case for p=2, when the group C_1K of all units of K, whose squares belong to C_K, is usually used instead of C_K. But C_1K is better only for index formula purposes, not having the other nice properties of C_K. The main aim of this paper is to offer another alternative to C_K which can be used in cyclotomic Z(p)extensions even for p=2 still keeping almost all nice properties of C_K. ER 
BULANT, Michal and Radan KUČERA. On a modification of the group of circular units of a real abelian field. \textit{Journal of Number Theory}. Elsevier, 2013, vol.~133, No~9, p.~3138  3148. ISSN~0022314X. doi:10.1016/j.jnt.2013.03.009.
