▁In ▁mathematics , ▁Sh af are v ich ' s ▁theorem ▁states ▁that ▁any ▁finite ▁sol v able ▁group ▁is ▁the ▁Gal ois ▁group ▁of ▁some ▁finite ▁extension ▁of ▁the ▁rational ▁numbers . ▁It ▁was ▁first ▁proved ▁by ▁, ▁though ▁Alexander ▁Schmidt ▁later ▁pointed ▁out ▁a ▁gap ▁in ▁the ▁proof , ▁which ▁was ▁fixed ▁by ▁. ▁ ▁References ▁▁▁▁ ▁Category : G alo is ▁theory ▁Category : Sol v able ▁groups <0x0A> </s> ▁Z ang ui ▁() ▁may ▁refer ▁to : ▁ ▁Z ang ui , ▁Ne h band an ▁ ▁Z ang ui , ▁Q a en <0x0A> </s> ▁Major ▁General ▁Juan ▁César ▁Cord ero ▁D áv ila ▁( J une ▁ 7 , ▁ 1 9 0 4 ▁– ▁July ▁ 2 0 , ▁ 1 9 6 5 ), ▁was ▁the ▁command ing ▁officer ▁of ▁the ▁ 6 5 th ▁Infantry ▁Regiment ▁during ▁the ▁Korean ▁War , ▁rising ▁to ▁become ▁one ▁of ▁the ▁highest ▁ranking ▁eth nic ▁officers ▁in ▁the ▁United ▁States ▁Army . ▁ ▁His ▁active ▁military ▁career ▁began ▁on ▁June ▁ 1 , ▁ 1 9 4 2 , ▁when ▁he ▁was ▁sum mon ed ▁to ▁serve ▁in ▁World ▁War ▁II . ▁On ▁January ▁ 2 , ▁ 1 9 5 2 , ▁he ▁was ▁re ass igned ▁to ▁Third ▁Infantry ▁Division ▁took ▁over ▁the ▁ 6 5 th , ▁command ing ▁them ▁along ▁a ▁set ▁of ▁Korean ▁and ▁Belg ium ▁batt al ions ▁and ▁pl ato on ▁from ▁Luxemb ourg . ▁He ▁also ▁served ▁as ▁an ▁S