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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 a Radan KUČERA. Annihilators for the class group of a cyclic field of prime power degree II. \textit{Canadian Journal of Mathematics}. Kanada, 2006, roč.~58, č.~3, s.~580-599. ISSN~0008-414X.
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