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Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups (Paperback)
Loot Price: R2,292
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Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups (Paperback)
Series: Memoirs of the American Mathematical Society
Expected to ship within 12 - 17 working days
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A characterization is given for the factorizations of almost simple
groups with a solvable factor. It turns out that there are only
several infinite families of these non-trivial factorizations, and
an almost simple group with such a factorization cannot have socle
exceptional Lie type or orthogonal of minus type. The
characterization is then applied to study s-arc-transitive Cayley
graphs of solvable groups, leading to a striking corollary that,
except for cycles, a non-bipartite connected 3-arc-transitive
Cayley graph of a finite solvable group is necessarily a normal
cover of the Petersen graph or the Ho?man-Singleton graph.
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