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@article{635805,
author = {Greither, Cornelius and Kučera, Radan},
article_location = {Kanada},
article_number = {3},
keywords = {Class group; annihilators; cyclic number field},
language = {eng},
issn = {0008-414X},
journal = {Canadian Journal of Mathematics},
title = {Annihilators for the class group of a cyclic field of prime power degree II},
volume = {58},
year = {2006}
}
TY - JOUR
ID - 635805
AU - Greither, Cornelius - Kučera, Radan
PY - 2006
TI - Annihilators for the class group of a cyclic field of prime power degree II
JF - Canadian Journal of Mathematics
VL - 58
IS - 3
SP - 580-599
EP - 580-599
SN - 0008414X
KW - Class group
KW - annihilators
KW - cyclic number field
N2 - We prove, for a field K which is cyclic of odd prime power degree over the rationals, that the annihilator of the quotient of the units of K by a suitable large subgroup (constructed from circular units) annihilates what we call the non-genus part of the class group. This leads to stronger annihilation results for the whole class group than a routine application of the Rubin-Thaine method would produce, since the part of the class group determined by genus theory has an obvious large annihilator which is not detected by that method; this is our reason for concentrating on the non-genus part. The present work builds on and strengthens previous work of the authors; the proofs are more conceptual now, and we are also able to construct an example which demonstrates that our results cannot be easily sharpened further.
ER -
GREITHER, Cornelius and Radan KUČERA. Annihilators for the class group of a cyclic field of prime power degree II. \textit{Canadian Journal of Mathematics}. Kanada, 2006, vol.~58, No~3, p.~580-599. ISSN~0008-414X.
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