The Held group, one of the twenty-six sporadic finite simple groups, bears the name of the German mathematician who identified its potential existence during the late 1960s. Dieter Held has spent his professional career exploring the logic and foundations of mathematics, primarily based within German academic institutions after completing his initial doctoral studies in Frankfurt.
Early Academic Formation
Born in 1936 in Berlin, Dieter Held pursued his higher education at Goethe University Frankfurt. Under the supervision of Reinhold Baer, he earned his Ph.D. in 1964. By 1962, his academic standing was such that he appeared as a speaker at the International Congress of Mathematicians, establishing his early presence in the global mathematical community.
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Following his doctoral graduation, Held moved to Australia for a series of lectureships. He served at the Australian National University starting in June 1965, remaining there until July 1966. Subsequently, he accepted a position at Monash University in Clayton, Victoria. He eventually resigned from this role to return to Germany, where he received a research fellowship from the Deutsche Forschungsgemeinschaft.
Discovery of the Held Group
In late 1968, Held investigated properties of an arbitrary finite simple group. His research focused on a centralizer of an involution isomorphic to the centralizer found in the center of a Sylow 2-subgroup of the Mathieu group M24. Graham Higman and John McKay later used computer methods to demonstrate that such a group existed. While their demonstration remained unpublished, Jörg Hrabe de Angelis later published a paper confirming the existence and uniqueness of the group.
Career at Mainz
Held joined the faculty of the Johannes Gutenberg University Mainz, where he spent the remainder of his active teaching career. He maintained his position at the Mathematics Institute of the university until his retirement in 2001. His work in the field of logic and foundations continued throughout his tenure in Mainz.
Fast facts
- Born: 1936, Berlin
- Citizenship: Germany
- Ph.D. Institution: Goethe University Frankfurt
- Doctoral Supervisor: Reinhold Baer
- Notable Discovery: Held group
- Primary Employer: Johannes Gutenberg University Mainz
- Retirement Year: 2001
Questions readers ask
What is the Held group?
It is one of the 26 sporadic finite simple groups identified by Dieter Held in 1968.
Where did Dieter Held conduct his research?
He worked in Germany at the Johannes Gutenberg University Mainz and held academic positions in Australia at the Australian National University and Monash University.
Achievements
- Held posts at Johannes Gutenberg University Mainz