Chessical: Ilivitsky was undoubtedly of Grandmaster strength, but being in the post war Soviet Union denied him the opportunity to obtain the title. He was far stronger than may of the "GM's" of today, but his career was largely confined to internal Soviet events.
Ilivitsky was born in 1921 and died in 1989. He became an IM in 1955 and was twice Russian champion in 1948 and 1949.I do not have a full record of Ilivitsky's accomplishments in tournaments, but from the cross tables in the collected games of other Soviet players I can provide this:
First in the 8th Russian championship 1948, 10th in the 16th USSR Championship 1948, first in the 9th Russian championship 1949, 7th in the 17th USSR Championship 1949, 6th in the Russian Championship 1950.
5th in the semi final of the 18th USSR Championship, 14th in the 20th USSR Championship, 15th in the 21st USSR Championship, 4th in the semi-final of the 22nd USSR Championship.
Then a sudden epiphany. He was <5th in the 22nd USSR Championship>. This was one of the strongest of all time with: Geller, Smyslov, Botvinnik, Petrosian, Spassky, Keres, Taimanov and Korchnoi (finished second to last) participating.
This qualified him for the the <Gothenberg Interzonal in 1955> where he scored +1 including a win over Geller. He later beat the Czech grandmaster Ludek Pachman in a play-off match.
He did not make it to the 1955 Soviet Championship coming 9th in the semi-final. Unable to sustain himself at the very top of the Soviet system, he lacked opportunities to play outside and gain a grandmaster title (in a similar way to Rashid Gibiatovich Nezhmetdinov).
I do not have a full record of his tournaments, but later highlights include a 6th at the Tchigorin Memorial in 1965.
I believe that died in very poor circumstances, and may have committed suicide.