JOHN BRITTON was a quiet, modest and private man who bore his distinction in his profession as a mathematician lightly. His work lay in Combinatorial Group Theory, a field whose roots go back to the turn of the century with the introduction of algebraic ideas into problems in geometry and topology.
A critical question in Combinatorial Group Theory is the 'word problem' - the problem of providing procedures which determine whether strings of symbols can be transformed, by specified substitution rules, known as group relations, into the empty string. Britton's first published work, from his 1953 doctoral dissertation, gave such procedures for a wide class of group relations.
After completing his thesis, Britton became aware of 'negative solutions' to the word problem, that is, examples of sets of group relations for which it was possible to prove that there could never exist a comprehensive procedure that would be applicable to all strings under consideration. By 1958 Britton was able to adapt his previous techniques to provide another negative solution. This work came to the attention of the American logician WW Boone, who invited Britton to spend the year 1961-62 at the University of Illinois in the United States.
The outcome of Britton's visit was his most influential paper, which appeared in 1963. By approaching Boone's own negative solution in a more free-ranging algebraic style than the traditional logician's approach, Britton was able to shorten and simplify the argument decisively. Although other approaches to the word problem were also found, Britton's has without doubt been the most widely applied by mathematicians from many countries.
Britton's academic career began at Beverley Grammar School and Hull University College, now Hull University. He did postgraduate work at Manchester University under the supervision of Bernhard Neumann and obtained the degree of Doctor of Philosophy in 1953. After National Service, he was a Research Fellow then Lecturer at Glasgow University from 1955 to 1966. In 1966 he became a Reader in Pure Mathematics at the University of Kent at Canterbury.
In the mid-1960s, Britton turned his attention to another important challenge for group theorists, the 'Burnside problem', first posed at the beginning of the 20th century by the English mathematician W. Burnside. The problem is to construct a certain type of group with infinitely many elements. Announcements in the Soviet literature had already indicated that there was activity in Moscow on this problem. After several years of unremitting labour, Britton finally published his construction in 1973 but, unfortunately, it was subsequently realised that there was a gap in the argument. Knowing that SI Adjan and PS Novikov had already published a proof, Britton chose not to expend more time on the issue.
Britton was appointed Professor of Pure Mathematics at Queen Elizabeth College, London University, in 1973. After the mergers amongst London colleges in 1985, he moved to King's College London. He retired in 1988 but continued part-time teaching until 1991. Britton served the mathematical community nationally as Meetings and Membership Secretary of the London Mathematical Society and editor of its newsletter from 1973 to 1976. He edited the volume on pure mathematics in the Collected Works of AM Turing which appeared in 1992.
John Britton was deeply distressed by the death of his wife, Catherine, in 1980 and the years did not diminish his sadness and sense of loss. He was consoled by their three daughters, Anne, Christine and Mary, to whom he was devoted.
(Photograph omitted)Reuse content