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A Characterization of the Finite Simple Groups PSp(4, q), G2(q), I

Published online by Cambridge University Press:  22 January 2016

Paul Fong  and
W.J. Wong
Paul Fong
Affiliation:
Tokyo University of Education
W.J. Wong
Affiliation:
Tokyo University of Education
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Suppose that G is the projective symplectic group PSp(4, q), the Dickson group G2(q)> or the Steinberg “triality-twisted” group where q is an odd prime power. Then G is a finite simple group, and G contains an involution j such that the centralizer C(j) in G has a subgroup of index 2 which contains j and which is the central product of two groups isomorphic with SL(2,q1) and SL(2,q2) for suitable ql q2. We wish to show that conversely the only finite simple groups containing an involution with this property are the groups PSp(4,q), G2(q)9. In this first paper we shall prove the following result.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 36 , November 1969 , pp. 143 - 184
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

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