In Greek, the PIE verbal roots *dheh1 'put' or 'do', *Hieh1 'throw', and *deh3 'give' show up with an unexpected -k- in some aorist forms: ἔθηκα, ἧκα, ἔδωκα. In Latin, the reflexes of the first two roots have -k- throughout: facio, iacio (although the present forms are new analogical formations, so it's plausible that this -k- too was once confined to the perfect/aorist). LIV adds some data from other Italic languages (and tentatively from Phrygian) but says the Greek and Italic -k-'s are unrelated (citing two references which I can't access at the moment), which seems odd. What are the theories as to the origin of this -k- or these -k-'s?

Also, are there other IE languages in which these verbs may have once had -k- in the aorist but we can't tell because the resulting forms would be the same with or without it? (For example, if Sanskrit once had an aorist *adhākt it seems plausible that the regular reflex of this, **adhāk, would be analogically reformed as the attested adhāt.)

In Greek, the PIE verbal roots *dheh1 'put' or 'do', *Hieh1 'throw', and *deh3 'give' show up with an unexpected -k- in some aorist forms: ἔθηκα, ἧκα, ἔδωκα. In Latin, the reflexes of the first two roots have -k- throughout: facio, iacio (although the present forms are new analogical formations, so it's plausible that this -k- too was once confined to the perfect/aorist). LIV adds some data from other Italic languages (and tentatively from Phrygian) but says the Greek and Italic -k-'s are unrelated (citing two references which I can't access at the moment), which seems odd. What are the theories as to the origin of this -k- or these -k-'s?

Also, are there other IE languages in which these verbs may have once had -k- in the aorist but we can't tell because the resulting forms would be the same with or without it? (For example, if Sanskrit once had an aorist *adhākt it seems plausible that the regular reflex of this, **adhāk, would be analogically reformed as the attested adhāt.)