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Abstract.
Let G be a finite
group and let 
be the set of elements of primary, biprimary
and triprimary order of G. We prove the following statement: if
the conjugacy class sizes of are exactly
with 
and 
, then G is
nilpotent and 
for some prime q. Some known results are generalized.
Received: 2012-05-04
Published Online: 2012-09-01
Published in Print: 2012-09-01
© 2012 by Walter de Gruyter Berlin Boston