1. CJM 2006 (vol 58 pp. 580)
 Greither, Cornelius; Kučera, Radan

Annihilators for the Class Group of a Cyclic Field of Prime Power Degree, II
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
nongenus part of the class group.
This leads to stronger annihilation results for the whole
class group than a routine application of the RubinThaine 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 nongenus 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.
Categories:11R33, 11R20, 11Y40 

2. CJM 1997 (vol 49 pp. 283)
 McCall, Thomas M.; Parry, Charles J.; Ranalli, Ramona R.

The $2$rank of the class group of imaginary bicyclic biquadratic fields
A formula is obtained for the rank of the $2$Sylow subgroup of the
ideal class group of imaginary bicyclic biquadratic fields. This
formula involves the number of primes that ramify in the field, the
ranks of the $2$Sylow subgroups of the ideal class groups of the
quadratic subfields and the rank of a $Z_2$matrix determined by
Legendre symbols involving pairs of ramified primes. As
applications, all subfields with both $2$class and class group
$Z_2 \times Z_2$ are determined. The final results assume the
completeness of D.~A.~Buell's list of imaginary fields with small
class numbers.
Categories:11R16, 11R29, 11R20 
