Vol. 30, No. 3, 1969

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Covering groups of groups of Lie type

John Moss Grover

Vol. 30 (1969), No. 3, 645–655

A construction for a central extension of a group satisfying a certain set of axioms has been given by C. W. Curtis. These groups are called groups of Lie type. The construction is based on that given by R. Steinberg for covering groups of the Chevalley groups. The central extensions constructed by Curtis, however, are not covering groups in the sense of being universal central extensions, as he shows by an example. Here, the Steinberg construction is considered for a more restricted class of groups of Lie type. It is shown that in this case, the central extension is a covering. It is also shown that this more restricted definition of groups of Lie type still includes the Chevalley and twisted groups, with certain exceptions.

Mathematical Subject Classification
Primary: 22.50
Received: 26 March 1968
Published: 1 September 1969
John Moss Grover