Vol. 75, No. 2, 1978

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ISSN: 0030-8730
Cohomology of degree 1 and 2 of the Suzuki groups

Gregory Wade Bell

Vol. 75 (1978), No. 2, 319–329
Abstract

Let V be the standard 4-dimensional module for Sz(q), the Suzuki group based on the field of q = 22n+1 elements. In this paper we determine H2(Sz(q),V ). This is usually (q 32) of dimension one (otherwise zero) and is generated by a cocycle which is the restriction of a generator of H2(Sp4(q),V ). In addition, the well known groups H2(Sz(q),GF(q)) and H1(Sz(q),V ) are calculated. The proof involves the use of the Hochschild-Serre spectral sequence to determine the cohomology of the normalizer of a Sylow 2-subgroup acting on the various one-dimensional modules involved.

Mathematical Subject Classification 2000
Primary: 20J06
Milestones
Received: 5 October 1976
Published: 1 April 1978
Authors
Gregory Wade Bell