#### Leading light in algebra research

**Karl Walter Gruenberg, mathematician: born Vienna 3 June 1928; Assistant Lecturer in Mathematics, Queen Mary College (later Queen Mary and Westfield), London University 1953-55, Lecturer 1957-61, Reader 1961-67, Professor of Pure Mathematics 1967-93 (Emeritus); Commonwealth Fund Fellow 1955-57; twice married (one son, one daughter); died London 10 October 2007.**

Karl Gruenberg, Emeritus Professor of Pure Mathematics of Queen Mary, London University, was a much respected algebraist, being a leading light in the London algebra research community, with many professional contacts across the globe.

Gruenberg was born in 1928 of Jewish parents in Vienna, where he spent his early life. His parents separated when he was still very young. After the Nazis took over, Karl and his parents all escaped, but separately, in different directions and at slightly different times. Karl got to the UK on a Kindertransport in 1939; arriving in England on his own at the age of 10 he was very unhappy, but fortunately his mother was able to join him later. He had a less than easy transition to the English school system, going first to Shaftesbury Grammar School in Dorset and then to Kilburn Grammar School in London.

Winning an entrance scholarship to Magdalene College, he went up to Cambridge, obtaining his BA in 1950 and his PhD in 1954. For the latter he worked under Philip Hall, the UK's leading algebraist at the time, submitting a thesis in the theory of groups (a branch of algebra concerned with an abstract study of symmetry). He moved to Queen Mary College, London University, temporarily in 1953 and permanently in 1957. There Kurt Hirsch was slowly building up a world-class algebra research centre and Gruenberg rapidly became a leading member of this group.

Gruenberg remained at Queen Mary all his working life, apart from leaves of absence mostly taken at North American universities. He was made Professor in 1967, and was Head of the Pure Mathematics Department from 1973 until 1978.

After leaving Cambridge he continued his research in abstract group theory into the 1960s, becoming a leading expert at the time on the Engel theory of groups, which is concerned with extracting global information from certain types of local data.

From about 1960 or so, his main research interest moved into homological algebra and its applications, particularly to group theory. In mathematics, frequently unsuspected connections arise between quite separate and apparently unrelated areas. In this work Gruenberg was concerned with applying to group theory techniques originally developed for the "geometry of continuity". In this field he was a major, in many ways the major, pioneer. This work led him over the years towards representation theory, especially integral representation theory, and more latterly number theory. He published many research articles both sing-ularly and jointly.

He was a talented and very successful teacher, especially of graduate students and his many innovative graduate courses were regularly attended by students, visitors and staff from Queen Mary and other London institutions. His books, Linear Geometry (1967, an undergraduate text written with Alan Weir), Cohomological Topics in Group Theory (1970) and Relation Modules of Finite Groups (1976), were all very well received. He continued his research to the end. He published a joint paper with Alfred Weiss in the Journal of Algebra in 2006, was working on further joint work with Weiss in the summer of 2007 both at Queen Mary and at the University of Alberta in Canada. He had been due to address the Queen Mary Pure Mathematics Seminar.

Gruenberg was a very cultured person with many interests well outside of mathematics. Particular interests of his were the theatre, music, architecture and painting. Years ago, I remember him as a pretty nifty left-handed table tennis player, though he always wrote with his right hand.

B.A.F. Wehrfritz

Published: 8 January 2008 © The Independent