Abelian Groups at New Mexico State University

Abstract

This is a description of some of the happenings in Abelian group theory at New Mexico State University (NMSU). This account is quite personal, and certainly has my own personal biases in it. Some of the players may feel slighted, for which I apologize. My excuses are simply bad memory and bad judgement. This account is supposed to explain how New Mexico State University became a center of Abelian group theory. At least it will describe some of the events and circumstances that I feel contributed to its development. There will be no attempt to detail who proved what particular theorem when, or to give a complete story of which areas were being emphasized at any particular time. Over the years, there were many Abelian group theorists at New Mexico State University doing many di¤erent things, and such a task would be overwhelming. Please keep these things in mind while reading this account. The ‡ourishing of Abelian group theory at New Mexico State was a product of several things. We had a sympathetic administration, both at the department level and at higher levels. Research money was readily available in the late 1950’s and 1960’s. And the subject was ready for development: Kaplansky’s book In nite Abelian Groups appeared in 1954, and Fuchs’book Abelian Groups appeared in 1958, and were tremendous catalysts. These circumstances and some good luck enabled us to attract some truly talented people. But how did this all get started, and how did New Mexico State continue to develop as a center of Abelian groups? It could be said that it was due to Professor W. R. Scott at the University of Kansas. At least four of his students came to NMSU after nishing at Kansas: Ralph Crouch, Delmar Boyer, me, and John Irwin, in that order. Boyer and I were recruited by Crouch, and I think John Irwin came because he wanted to go somewhere where there was another Abelian group theorist, and Professor Scott knew us. I came to NMSU in 1957, and Irwin in 1960. John was a very special person. He was intense, and totally devoted to the subject. He and I worked together for several years, at rst on his topic of high subgroups. I think John had as much to do with New Mexico State University becoming a center of Abelian groups as anyone. It was John who suggested that we apply for National Science