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Lifting wreath product extensions |
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| Authors: | Elena V Black |
| Institution: | Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019 |
| Abstract: | Let |
| Keywords: | |
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and 
be finite groups and let 
be a hilbertian field. We show that if 
has a generic extension over 
and 
satisfies the arithmetic lifting property over 
, then the wreath product 
of 
and 
also satisfies the arithmetic lifting property over 
. Moreover, if the orders of 
and 
are relatively prime and 
is abelian, then any extension of 
by 
(which is necessarily a semidirect product) has the arithmetic lifting property.