A Characterization of the Finite Simple Groups PSp(4, q), G2(q), I
- 1 November 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 36, 143-184
- https://doi.org/10.1017/s0027763000013180
Abstract
Suppose that G is the projective symplectic groupPSp(4, q), the Dickson groupG2(q)>or the Steinberg “triality-twisted” groupwhereqis an odd prime power. Then G is a finite simple group, andGcontains an involutionjsuch that the centralizerC(j)inGhas a subgroup of index 2 which containsjand which is the central product of two groups isomorphic withSL(2,q1)andSL(2,q2)for suitableqlq2.We wish to show that conversely the only finite simple groups containing an involution with this property are the groupsPSp(4,q), G2(q)9.In this first paper we shall prove the following result.Keywords
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