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A characterisation of PSL2(Zþλ) and PGL2(Zþλ)
Published online by Cambridge University Press: 09 April 2009
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Let Fq denote the finite field with q elements, Zm the residue class ring Z/mZ. It is known that the projective linear groups G = PSL2(Fq) and PGL2(Fq) (q a prime-power ≥ 4) are characterised among finite insoluble groups by the property that, if two cyclic subgroups of G of even order intersect non-trivially, they generate a cyclic subgroup (cf. Brauer, Suzuki, Wall [2], Gorenstein, Walter [3]). In this paper, we give a similar characterisation of the groups G = PSL2 (Zþt+1) and PGL2 (Zþt+1) (p a prime ≥ 5, t ≥ 1).
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- Copyright © Australian Mathematical Society 1968
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