Etymology
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omo- 

before vowels om-, word-forming element meaning "raw, unripe," from Greek ōmos "raw," from PIE root *hemo- "raw, sharp-tasting" (source also of Sanskrit amah "raw, uncooked, unripe," Armenian hum; Old Irish om, Welsh of).

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lacto- 
before vowels, lac-, word-forming element used in chemistry and physiology from 19c. and meaning "milk," from Latin lac (genitive lactis) "milk," from Proto-Italic *(g)lagt-, from PIE root *g(a)lag- "milk." This and the separate root *melg- (source of milk (n.)) account for words for "milk" in most of the Indo-European languages. The absence of a common word for it is considered a mystery. Middle Irish lacht, Welsh llaeth "milk" are loan words from Latin.
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-ish 
adjectival word-forming element, Old English -isc "of the nativity or country of," in later use "of the nature or character of," from Proto-Germanic suffix *-iska- (cognates: Old Saxon -isk, Old Frisian -sk, Old Norse -iskr, Swedish and Danish -sk, Dutch -sch, Old High German -isc, German -isch, Gothic -isks), cognate with Greek diminutive suffix -iskos. In its oldest forms with altered stem vowel (French, Welsh). The Germanic suffix was borrowed into Italian and Spanish (-esco) and French (-esque). Colloquially attached to hours to denote approximation, 1916.

The -ish in verbs (abolish, establish, finish, punish, etc.) is a mere terminal relic from the Old French present participle.
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