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Poplavsky was born in Imperial Russia, in Podolia. His family (his father's name was Hilary) was ethnically Polish, and in his younger years he considered himself a Pole. He was a member of the Communist Party of the Soviet Union from 1930 onwards.
He was drafted to the Red Army in 1920 and served for the first three years (until 1923) as a private, then for four years (until 1927) as an NCO, company commander in the 297th Rifle Regiment. Over the next few years he attended an officer school, and afterwards received his own commands: first of a platoon in the 137th Rifle Regiment (1930–1931), then a platoon (1931–1933) and later a company in the School for Infantry Officers in Kharkov (1933–1935).
Before the Second World War he attended the Frunze Military Academy (1935–1938) where he became an instructor of military tactics (1938–1939) but in February 1939 he was relieved after a false accusation and given a manager's job at a sovkhoz.
He returned to service shortly before the German invasion of the Soviet Union. He was first a member of the staff of the 162nd Rifle Division, next commander of 720th Rifle Regiment (July–September 1941), and then Chief of Staff of 363rd Rifle Division (October 1941 – January 1942). During the next four months he commanded the 184th, 256th and 220th Rifle Divisions, and then the 45th Rifle Corps in the Soviet 5th Army (June 1943 – September 1944).
In 1944 he was transferred to the Ludowe Wojsko Polskie (Polish People's Army) as one of the many Soviet officers who were to ensure that this allied formation remained loyal to communist ideals. As major general he commanded the Polish Second Army (26 September – 19 December 1944) and later the Polish First Army (till 10 September 1945). His units took parts in the breakthrough of the Pommernstellung (Pomerania Wall) fortification line, securing the Baltic Sea coast, crossing the Odra and Elbe rivers and the battle of Berlin. He was wounded four times in the war.
After the war he remained in the Polish army, along with thousands of other ethnically-Polish Soviet officers, including Konstantin Rokossovsky, who were put in charge of almost all Polish military units, either as commanding officers or as their advisors. Poplavsky served as commander of the Polish forces occupying Germany, later being commander of the Silesian Military District (until 22 November 1947), Chief Commander of the Polish Land Forces (until 21 March 1950), and General Inspector of Military Training (until 2 April 1949). He also held political positions: on 2 April 1949 he became the 2nd Deputy Minister of National Defence and later was Deputy Minister himself. He was also a deputy to the Polish Sejm (1947–1956), and from 1949 to 1956 he was a member of the Central Committee of the Polish United Workers Party (PZPR).
In 1956 he was commander of the military forces responsible for the suppression of the Poznań 1956 protests. Afterwards, with the beginning of the era of destalinization, he (together with a significant number of other Soviet officers) left the Polish Army, which was granted slightly increased independence, and returned to the Soviet Union, where he became the 1st Deputy of the Chief Inspector of Military Training of the Red Army, and from 1958 an advisor to the inspectors-general of the Soviet Ministry of Defense.
Poplavsky was the recipient of many awards, including Polish (Commander Cross of the Order of Virtuti Militari, Cross of Grunwald Second Class) and Soviet (Hero of the Soviet Union, Order of Lenin (3 times), Order of Suvorov (I and II Class), Order of Kutuzov (II Class), Order of Bogdan Khmelnitsky (II Class) and Order of the Red Banner (4 times)). Several items were named after him, particularly in the People's Republic of Poland, including a ship of the Polish Merchant Navy.
- Wound Decoration, 7 times
- Commander's Cross of the Order of Virtuti Militari
- Grand Cross of the Order of Polonia Restituta (previously awarded Commander and Commander with Star)
- Cross of Grunwald, 2nd class
- Order of the Banner of Work, twice
- Gold Cross of Merit, twice
- Silver Medal in the Service of the Armed Forces of the Homeland
- Bronze Medal in the Service of the Armed Forces of the Homeland
- Silesian Uprising Cross
- Warsaw Medal 1939–1945
- Medal for Odra, Nysa, Baltic Sea
- Medal of Victory and Freedom 1945
- Medal "10th Anniversary of People's Poland"
- Medal "For participation in the battle for Berlin"
- Medal "Brotherhood in Arms"
- "Gold Star" Medal, Hero of the Soviet Union (29 May 1945)
- Order of Lenin, three times
- Order of the October Revolution
- Order of the Red Banner, four times
- Order of Suvorov, 1st and 2nd classes
- Order of Kutuzov, 2nd class
- Order of Bogdan Khmelnitsky, 2nd class
- Order of the Red Star
- Medal "For the Defence of Moscow"
- Medal "For the Liberation of Warsaw"
- Medal "For the Capture of Berlin"
- Jubilee Medal "In Commemoration of the 100th Anniversary since the Birth of Vladimir Il'ich Lenin"
- Medal "For the Victory over Germany in the Great Patriotic War 1941–1945"
- Jubilee Medal "Twenty Years of Victory in the Great Patriotic War 1941-1945"
- Jubilee Medal "30 Years of the Soviet Army and Navy"
- Jubilee Medal "40 Years of the Armed Forces of the USSR"
- Jubilee Medal "50 Years of the Armed Forces of the USSR"
- Military Order of the White Lion, 1st class (Czechoslovakia)
- Gold Star of the Czechoslovak Military Order for Liberty (Czechoslovakia)
- Distinguished Service Cross (United States)
- Chief Commander of the Legion of Merit (USA)
- Order of the Partisan Star, First Class (Yugoslavia)
- Order of Courage (Yugoslavia)
Author of memoirs "Comrades of the front roads" (or "Comrades of the struggle"; Polish title: Towarzysze frontowych dróg, Warszawa 1964, 1966, 1970, 1973, 1983; Russian title: Товарищи в борьбе', Moskwa 1963, 1974; German title: Kampfgefährten, Berlin 1980). The original title was to be "On the land of forefathers" (Na ziemi przodków, За землю предков), but it was changed by the censors.
- (in Polish) Short biography on the page of Silesian Military District
- Timeline of military career
- (in Russian) Comrades in the Struggle, memoirs of Poplavsky