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Graphs with Projective Linear Stabilizers

✍ Scribed by K. Ching

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 227 KB
Volume: 20
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1998.0263

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✦ Synopsis

We investigate the structure of the free amalgamated product P 1 * P 1 ∩P 2 P 2 in which P 1 and P 2 are isomorphic projective linear groups and P 1 ∩ P 2 is a one-point stabilizer in the natural action of P i on the points of a projective space of dimension n ≥ 2. We apply the results to graphs admitting a vertex-transitive automorphism group such that the subgroup stabilizing a vertex is a projective linear group. In particular, graphs of girth 4 with projective linear stabilizers are characterized.

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