Walter Feit (1930–2004) Leonard Scott, Ronald Solomon, John Thompson, John Walter, and Efim Zelmanov alter Feit died on July 29, 2004, at “Walter Feit was born in Vienna, Austria, in 1930. age seventy-three after a long ill- In August of 1939 his parents saved his life by ness. He had been on the faculty at placing him on the last train (KinderTransport) Yale for forty years, and the follow- allowed to carry Jewish children out of Austria. He Wing is taken from his obituary at the arrived in England just as the British government Yale website. It summarizes Walter’s achievements was evacuating all children from London. After and stature, and provides touching detail on Wal- being relocated a few times, he settled in a refugee ter’s childhood during the Second World War. hostel in Oxford. In 1943 he won a scholarship to “Professor Feit’s 1963 paper with John G.Thomp- an Oxford technical high school. His teachers were son, ‘Solvability of groups of odd order’, filled an very encouraging, and he recorded that it was at this entire issue of the Pacific Journal of Mathematics time that he became ‘passionately interested in and is widely regarded as the most influential paper mathematics’. ever written on finite group theory. It energized the “In 1946 Walter moved to the United States to field, providing both inspiration and technical tools stay with an aunt and uncle. In a letter recovered for the research that finally culminated in the from the time of his arrival in New York, he complete classification of simple finite groups. poignantly describes his first experiences of the “Finite group theory was only one of several new world; see http://www.math.yale.edu/ areas invigorated by Professor Feit’s insights. His public_html/WalterFeit/ToNewYork/ paper with Graham Higman became a fundamen- Welcome.html. tal building block and stimulated a large body of “The following September he entered the research on combinatorial structures. His work on University of Chicago and joined its energetic Schur indices revitalized progress in that subject mathematical community. Within four years he as well. had obtained the university’s master’s degree in “Feit joined the Yale faculty of mathematics in mathematics; he later received his Ph.D. from the 1964. He served the Yale mathematics department University of Michigan. In 1953, at the age of twenty- in several administrative roles, acting as director of two, he joined the Cornell University mathematics undergraduate studies, director of graduate stud- faculty. ies, and chairman. His standing in the mathematics “Walter Feit visited Oxford University many community was marked by award of the American times, but the 1990 International Symposium on Mathematical Society Cole Prize in Algebra, election the Inverse Galois Problem held there at University to the National Academy of Sciences and the Amer- College in honor of his sixtieth birthday was an ican Academy of Arts and Sciences, editorship of especially joyful occasion. various journals, and vice presidency of the Inter- “In October 2003, on the eve of Professor Feit’s national Mathematical Union. retirement, colleagues and former students 728 NOTICES OF THE AMS VOLUME 52, NUMBER 7 gathered at Yale for a special four-day Conference for all those whom it on Groups, Representations and Galois Theory to touched as victims. honor him and his contributions. Nearly eighty But this was a part of researchers from around the world met to ex- history which caught change ideas in the fields he had helped to create. up with him in his “Professor Feit is survived by his wife, Dr.Sidnie youth without giving Feit, of Hamden, Connecticut; his son, professor of him any choice. mathematics Paul Feit, of Odessa, Texas; and his Walter had earned daughter, artist Alexandra Feit, of Haines, Alaska. A bachelor’s and mas- memorial service was held on Sunday, October 10, ter’s degrees from the 2004, at the New Haven Lawn Club, 193 Whitney University of Chicago. Avenue, New Haven, CT.” Because of his inter- This memorial article presents five contribu- ests, his advisors rec- tions, in rough historical order, from mathemati- ommended he go to cians commenting on Walter, both mathematically Michigan, where and personally, at various times in his career, Richard Brauer was on all mentioning the odd order paper. These are the faculty. Michigan followed by some quoted excerpts from remarks was an attractive place delivered by Walter’s Yale colleagues George Selig- for us to be. T. H. man, Roger Howe, and Dan Mostow at the memo- Hildebrandt was then rial service. Another selection from that service, by chairman and had Shreeram Abhyankar, is included in a section on built up the depart- Walter Feit Walter’s later years. Walter’s graduate students ment, appointing and postdocs, and the conferences and volumes Brauer just after the written in his honor are listed in a final section. end of World War II. There was a lot of interesting —Len Scott activity in many fields. For example, Raoul Bott was starting his career there and was a focus of at- The first contribution is from John Walter, who tention. Raymond Wilder was the leader in topol- ogy. Also active were Edwin Moise and Hans was Walter Feit’s roommate during part of their time Samelson. R. M. Thrall was working on the theory together at Michigan. John was himself a major of rings. Among the junior faculty were Jack player in the coming developments regarding groups MacLaughlin, whom I knew from Caltech, and Alex of even order and the early days of the Classifica- Rosenberg, who had just come from Chicago. tion, especially in his work with Gorenstein. John Walter stood out, having done well in an ad- takes us from the days at Michigan to the Chicago vanced and very competitive mathematics program group theory year, 1960–61, where much of the at Chicago led by an outstanding faculty. I am not work on the odd order paper, cited above, was done. sure what aroused his interest in group theory, but The Early Years I remember knowing that he was advised to go to Michigan to work with Brauer. He reflected the John H. Walter feisty and competitive spirit that existed at Chicago, along with a sense of fellowship among the un- I would like to look back to the early years of a fifty- dergraduate math students, and he carried this three-year friendship with Walter Feit in an effort over to Michigan. At the basis of this was an ethic to remember and convey the circumstances of his that valued good work and a profound respect for first years as a mathematician. I met Walter in the mathematics as a discipline. I remember the some- fall of 1951 at the University of Michigan, where what presumptuous discussions about who was we both had entered graduate school. He was the more important algebraist, André Weil or born in Austria and had emigrated first to England Richard Brauer. But I have always felt that the and then to the United States, where he was raised basis for this impertinence was Walter’s strongly in Miami by an aunt and uncle. His parents were felt respect for mathematical accomplishment and unable to obtain a visa and vanished in the Holo- a loyalty to institutions that served him well in his caust. He never spoke much about this. I did not career. Because of our common interest, there was understand why at the time. However, it was clear a lot to talk about. then and more clear now that he had a sense of The group theory program at Michigan being history, and mathematics gave him the opportunity led by Brauer certainly fulfilled our expectations. to participate. The Holocaust was certainly a tragedy His seminar was on the modular representations of finite groups, a subject which he initiated. This John H. Walter is retired from the department of mathe- was a stimulating and memorable event in a very matics at the University of Illinois, Urbana-Champaign. His exciting year. Walter additionally took an informal email address is [email protected]. AUGUST 2005 NOTICES OF THE AMS 729 reading course from Brauer on class field theory. exceptional character theory of groups containing In the summer of 1952 Brauer invited Michio Suzuki Frobenius groups as subgroups. In the meanwhile, to Michigan for a few weeks. He talked in the sem- Suzuki, using the exceptional character theory, inar on his recent thesis [9], in which he charac- had proved the solvability of finite groups of odd terized the linear fractional groups PSL(2,p). His order in which the centralizer of every nonidentity argument was based on character theory, where he element was abelian [10]. This result was published focused on a particular class of irreducible char- in 1957. Then in 1959 John Thompson finished acters, called exceptional characters, which are pre- his thesis at Chicago, in which he developed some sent when there exist subgroups of a simple group new techniques in constructing maximal subgroups whose conjugates intersect only in the identity sub- containing Sylow groups. He also noted the rele- group. A great deal of information about these ir- vance of Feit’s work on exceptional character reducible characters can be obtained directly from theory that is associated with Frobenius groups. the irreducible characters of these subgroups and Based on [3], [4], [5], and the methods of John’s the characters that they induce. It was clearly an im- thesis [11], they saw the possibility of extending portant concept, and it seemed to us that it might Suzuki’s work to show the solvability of finite open up a new direction that could be usefully ex- groups of odd order.