before vowels sarc-, word-forming element in science meaning "flesh, fleshy, of the flesh;" from Latinized form of Greek sark-, combining form of sarx "flesh," traditionally derived from a PIE root *twerk-, *tuerk- "to cut" (source also of Avestan thwares "to cut"), but Beekes is dubious.
word-forming element meaning "division; split, cleavage," from Latinized form of Greek skhizo-, combining form ("irregular," says OED) of skhizein "to split, cleave, part, separate" (from PIE root *skei- "to cut, split").
word-forming element meaning "quality, condition; act, power, skill; office, position; relation between," Middle English -schipe, from Old English -sciepe, Anglian -scip "state, condition of being," from Proto-Germanic *-skepi- (cognates: Old Norse -skapr, Danish -skab, Old Frisian -skip, Dutch -schap, German -schaft), from *skap- "to create, ordain, appoint," from PIE root *(s)kep-, forming words meaning "to cut, scrape, hack" (see shape (v.)). It often forms abstracts to go with corresponding concretes (friend/friendship, etc.).