The Wikipedia article also refers to Carlo Zaniolo's new definition of 3NF, which is provably equivalent to the original definition, and that was the definition I was using - it's much simpler, easier to explain, and easier to see the relationship between 3NF, EKNF, and BCNF when you use Zaniolo's definition. If you prefer to think in terms of the original definition, there is a transitive dependency there: City -> Group (because of the stated business rules that only one group has a depot in any given city - but anyway as (City) is a candidate key we know that City -> Group is an FD of this relation) and Group -> Phone number (because of the stated business rule that each group uses a single order phone number); and the partition of the table represents the Group -> Phone number FD in a separate table, removing Phone number from the original table to eliminate the transitive FD.

Even in 1NF every attribute, prime or not, is dependent on every superkey (that's the definition of a superkey) and hence on every candidate key (as a candidate key is a minimal superkey). The difference between 2NF and 3NF is that 2NF does not permit any non-prime attribute to have a dependency on something which is a proper subset of a candidate key, while in 3NF a non-prime attribute may not depend on anything which is not a superkey (2NF says "the whole key" while 3NF says "nothing but the key").

I hope the above is clear enough - if not, get back to me and I'll try again.

Regards

Tom