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A characterisation of PSL2(Zþλ) and PGL2(Zþλ)

Published online by Cambridge University Press:  09 April 2009

G. E. Wall
G. E. Wall
Affiliation:
University of Sydney and University of Warwick
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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).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 3 , August 1968 , pp. 523 - 543
Copyright
Copyright © Australian Mathematical Society 1968

References

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