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A Characterization of PSL(2, 31) and its Geometry

Published online by Cambridge University Press:  20 November 2018

Manley Perkel
Manley Perkel*
Affiliation:
Wright State University, Dayton, Ohio
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The aim of this paper is the characterization of PSL(2, 31) in terms of its action on a certain polygonal graph. A polygonal graph is a pair (, ) consisting of a graph which is regular, connected and has girth m for some m ≧ 3, and a set of m-gons (circuits of length m) of such that every 2-claw (i.e. path of length 2) of is contained in a unique element of , (See Section 2 for the definitions of the terms used here.) If is the set of all m-gons of H, so that there is in a unique m-gon on every one of its 2-claws, then we write for (, ) and call a strict polygonal graph. If we wish to emphasize the integer m, then we call (, ) an m-gon-graph (respectively, a strict m-gon-graph). For convenience, a strict 5-gon-graph will be called a pentagraph.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 1 , 01 February 1980 , pp. 155 - 164
Copyright
Copyright © Canadian Mathematical Society 1980

References

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