the cat

We learn the cat was brought to Europe from Egypt and this is
why there should not be an IE-radical for this animal.
Is this indeed true?There was no cat in Europe until the
phoenicians brought some in 900 BC from Egypt to Europe?
Let see some languages here and what the word "cat" means in
each one

French=Chat ,Welsh=Cath ,Polish=Kot ,Sanskrit=Puccha
,Persia=Pushak ,Italian=Gatto ,Spanish=Gato,
Lithuanian=Puize ,German=Katze ,Russian=Kots ,Irish=Pus , Rom
=pisica, latin= felis
As a first observation we will see there seems to be two
groups .
One with "k:t" and one with "p:s"
chat, cath, kitt, gato, katze, kots, kot
pushak, pus, pis (rom. -ica from pisica is the diminitiv ,
generaly "ica" beeing a dimunitiv making suffix in romanian)

I just ask because there are big similarities for the name of
this word and second, because there seems indeed to be grouped
in two groups.
I asked myself what to do with the latin word "felis". I
cannot put it in the group with "k:t" but if I think that
*bh>f in most cases in latin language and in romanian an P-
dialects from galic "bh>b(p), then I should have the tendency
to
put the latin "felis" in the group with "p:s"

Any ideea about?