4-Engel groups are locally nilpotent

Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.

Group portrait at the farewell banquet for Dr. William Antopol from the laboratory staff of Mount Sinai Hospital; Ken's Chop House, New York city Portraits Groups

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Group US Army military portrait including Dr. William Levison (top row, third from left); Schofield Barracks, Hawaii Portraits Groups Men

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U.S. Army Passover Seder; Hawaii Portraits Groups

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Dr. William Levison (seated, far left) with other U.S. Army medial doctors and nurses with Christmas Tree in background Portraits Groups

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Unterprima (eleventh grade) boys school class portrait Portraits Groups Men

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Group portrait at the farewell banquet for Dr. William Antopol from the laboratory staff of Mount Sinai Hospital; Ken's Chop House, New York city Portraits Groups

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Group US Army military portrait including Dr. William Levison (top row, third from left); Schofield Barracks, Hawaii Portraits Groups Men

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U.S. Army Passover Seder; Hawaii Portraits Groups

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Unterprima (eleventh grade) boys school class portrait Portraits Groups Men

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Dr. William Levison celebrating Christmas Eve with U.S. Army buddies; Schofield Barracks, Hawaii Portraits Groups Men

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Dr. William Levison with U.S. Army buddies; Schofield Barracks, Hawaii Portraits Groups Men

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Group portrait, 2nd reunion of the World War II 75th Station Hospital; Hotel Governor, Clinton, New York Portraits Groups

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Group portrait, welcome home dinner for ex-service personnel; Newark Beth Israel Hospital; Hotel Essex House, Newark, New Jersey Portraits Groups

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Group portrait, testimonial dinner for Dr. Paul Klemperer's 10th anniversary at Mt. Sinai Hospital given by his students; Cavanagh's, New York City Portraits Groups

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