Why are Proto-Germanic *taikijaną and Proto-Indo-European *deyḱ- cognate? I don't understand why are PGmc k and Proto-Indo-European ḱ cognate?
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1I edited because you missed that it was palatal in PIE. I'm not sure if it makes a difference--not really, if the plain and velar fell together in Centum languages early on.– vectoryAug 30, 2020 at 2:20
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The *k might be explainable as the reflex of a Pre-Proto-Germanic geminate *-kk- that simplified to *k after a heavy syllable.
There is a disputed proposed sound law "Kluge's law" that derives geminates like -kk- from PIE sequences of plosive + *n (when the *n starts an accented syllable). I don't know whether there is any plausible source of *n in this word.
The alternative explanation of the source of geminate plosives in Germanic is "expressive lengthening".
answered Aug 29, 2020 at 22:06
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Fulk 2018 §6.9: Ringe is a staunch opponent to Kluge's Law; others fully accept it. The problem after Fulk seems to be that "Dating Kluge's Law to PGmc. also means that the effects of the law should be evident in Gothic." what's an orthographic feature; or Gothic reversed the effects. "... geminate obstruents are exceedingly few in Gothic and are found probably only in borrowed words and in names;" -- direct transliterations? No sure counter-evidence is shown, "some counterexamples to the law in Gothic are likely to show root accent," inhibiting the effect, "in others this is not so plain" …– vectoryAug 30, 2020 at 11:31
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… and it's odd that some evidence is completely missing: " Although much analogical disruption must be assumed, Kluge’s findings also provide a means of accounting for the coöccurrence of the stems *ob- and *upp- (the latter, strikingly, unreflected in Gothic) in certain forms …". Fulk repeatedly stresses that analogical disruption must be assumed. Opponents might rather see independent innovations. While Gothic shows reflexes of *deyḱ- with ungeminate h, there's no direct cognate to teacher anywhere, unless Ger. Erzieher is admitted (supperficially ziehen "to draw, pull, raise").– vectoryAug 30, 2020 at 11:50
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The root paradigm seems to have fallen appart or become suppletive. Distant cognates, as it were, do exhibit the necessary -n-, e.g. Ger. Zeichnung, Zeich'n, AGr. δείκνῡμ. Ger. Zeugniss maybe suspect of foreign influence (cp. signature, testament, confession, witness for semantics). Further cp. Zigeuner, likely from AGr. Τσιγγάνοι, contrast Gauner "thug": "with East Middle German g- for the j- sound of older Joner, … probably … from West Yiddish יוון (Yovon, “Greece”), יוונער (yevoner, “Greek, Ionian”), … Hebrew יָוָן (yaván, “Greece”). The exact origin is unclear." [WT]– vectoryAug 30, 2020 at 12:06