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Grouping similar indices together in an expression


Hi,

I am a newbie in Mathematica, and am trying to do the following.

I have terms which look like
a[i] a[j] b[i] b[j]

I need to apply a function F, for which I need to group the different
indices (by which I mean i, j) together as follows:

F(a[i] a[j] b[i] b[j]) = F(a[i] b[i]) F(a[j] b[j])

I do not in general know how many different indices there might be in a
term.  E.g. I might have
a[i] a[j] a[k] b[j]

Could somebody please give me a hint as to how to do this?

Thanks,
David.


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