▁frequently ▁cred ited ▁to ▁, ▁though ▁the ▁finit ely ▁generated ▁case ▁is ▁sometimes ▁instead ▁cred ited ▁to ▁; ▁details ▁follow . ▁ ▁Group ▁the or ist ▁L ász ló ▁F uchs ▁states : ▁ ▁The ▁fundamental ▁theorem ▁for ▁finite ▁ab elian ▁groups ▁was ▁proven ▁by ▁Leopold ▁Kr one cker ▁in ▁, ▁using ▁a ▁group - the or etic ▁proof , ▁though ▁without ▁stating ▁it ▁in ▁group - the or etic ▁terms ; ▁a ▁modern ▁presentation ▁of ▁Kr one cker ' s ▁proof ▁is ▁given ▁in ▁, ▁ 5 . 2 . 2 ▁Kr one cker ' s ▁Theorem , ▁ 1 7 6 – 1 7 7 . ▁This ▁generalized ▁an ▁earlier ▁result ▁of ▁Carl ▁Friedrich ▁G auss ▁from ▁Dis quisition es ▁Ar ithmet ica e ▁( 1 8 0 1 ), ▁which ▁class ified ▁quadratic ▁forms ; ▁Kr one cker ▁c ited ▁this ▁result ▁of ▁G auss ' s . ▁The ▁theorem ▁was ▁stated ▁and ▁proved ▁in ▁the ▁language ▁of ▁groups ▁by ▁Ferdinand ▁Georg ▁Fro ben ius ▁and ▁Ludwig ▁St ick el berger ▁in ▁ 1 8 7 8 . ▁Another ▁group - the or etic ▁form ulation ▁was ▁given ▁by ▁Kr one cker ' s ▁student ▁Eugen ▁N etto ▁in ▁ 1 8 8 2 . ▁ ▁The ▁fundamental ▁theorem ▁for ▁finit ely ▁presented ▁ab elian ▁groups ▁was ▁proven ▁by ▁Henry ▁John ▁Stephen ▁Smith ▁in ▁, ▁as ▁integer ▁matrices ▁correspond ▁to ▁finite ▁present ations ▁of ▁ab elian ▁groups ▁( this ▁general izes ▁to ▁finit ely ▁presented ▁modules ▁over ▁a ▁principal ▁ideal