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Superimprimitive 2-generator finite groups

Published online by Cambridge University Press:  20 January 2009

A. M. Macbeath
A. M. Macbeath
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.
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In his thesis, A. A. Hussein Omar, motivated by the study of possible shapes of generic Dirichlet regions for a surface group, made a detailed study for g = 2,3 of the groups generated by pairs (μ, τ) of regular (i.e. fixed-point-free) permutations of order 2,3 respectively and of degree n = 6(2g − 1), such that μ ْ τ is an n-cycle. He observed that, for g = 2,3, precisely one pair generates what he calls a superimprimitive group, and raised the question whether such pairs exist for all g, and, if so, whether they areunique. Our main result is that they do always exist, but that, for large values of g, theyare far from unique. (For details and some motivation for the notation, see [4, 5].)

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 1 , February 1987 , pp. 103 - 113
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

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